Universität Duisburg-Essen

Mathematik, Campus Essen

Diplom:
1. Die zahme Fundamentalgruppe einer ebenen Quartic mit drei Spitzen, Heidelberg 1972.
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Dissertation:
1. Invarianten der degenerierten Fasern in lokalen Familien von Kurven, Mannheim 1975.
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Articles:
1. Invarianten der degenerierten Fasern in lokalen Familien von Kurven. Journ. reine angew. Math. 293/294 (1977) 284 - 308 (Résumé of the thesis)
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2. 
   Rational singularities of higher dimensional schemes. Proc. AMS 63 (1977) 6 - 8
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3. 
   Canonical divisors and the additivity of the Kodaira dimension for morphisms of relative dimension one. Compositio Math. 35 (1977) 197 - 223
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   Erratum: Compositio Math. 35 (1977) 336
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4. 
   Klassifikationstheorie algebraischer Varietäten der Dimension drei, Compositio math. 41 (1980) 361 - 400 (Habilitation, Mannheim, 1980)
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5. 
   (with Y. Kawamata) On a characterization of an abelian variety in the classification theory of algebraic varieties. Compositio math. 41 (1980) 355 - 359
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6. 
   Die Additivität der Kodaira Dimension für projektive Faserräume über Varietäten des allgemeinen Typs. Journ. reine angew. Math. 330 (1982) 132 - 142
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7. 
   Vanishing theorems. Journ. reine angew. Math. 335 (1982) 1 - 8
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8. 
   (with H. Esnault) Revêtement cycliques. Algebraic Threefolds, Proc. Varenna 1981. Springer Lect. Notes in Math. 947, 241 - 250
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9. 
   (with H. Esnault) Sur une minoration du degré d'hypersurfaces s'annulant en certains points. Math. Ann. 263 (1983) 75 - 86
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10. 
    Weak positivity and the additivity of the Kodaira dimension for certain fibre spaces. Proc. Algebraic Varieties and Analytic Varieties, Tokyo 1981. Adv. Studies in Math. 1, Kinokunya-North-Holland Publ. 1983, 329 - 353
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11. 
    Weak positivity and the additivity of the Kodaira dimension II: the local Torelli map. Proc. Classification of Algebraic and Analytic Manifolds, Katata 1982. Progress in Math. 39, Birkhäuser 1983, 567 - 589
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12. 
    (with H. Esnault) Dyson's lemma for polynomials in several variables (and the theorem of Roth). Inventiones math. 78 (1984) 445 - 490
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13. 
    (with H. Esnault) Two dimensional quotient singularities deform to quotient singularities. Math. Ann 271 (1985) 439 - 449
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14. 
    (with H. Esnault) Revêtements cycliques II, Proc. Algebraic Geometry, La Rabida 1984, Hermann, Travaux en cours 23 (1987) 81 - 96
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15. 
    (with H. Esnault) Logarithmic De Rham complexes and vanishing theorems. Inventiones math. 86 (1986) 161 - 194
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16. 
    (with H. Esnault) Deligne-Beilinson cohomology. in: Beilinson's Conjectures on Special Values of L-Functions ( Ed.: Rapoport, Schappacher, Schneider ). Perspectives in Math. 4, Academic Press (1988) 43 - 91
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17. 
    (with H. Esnault) A remark on a non-vanishing theorem of P. Deligne and G.T. Mostow. Journ. reine angew. Math. 381 (1987) 211 - 213
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18. 
    (with H. Esnault) Vanishing and non-vanishing theorems. Proc. Hodge Theory, Luminy 1987 (Ed.: Barlet, Elzein, Esnault, Verdier, Viehweg). Astérisque 179 - 180 (1989) 97 - 112
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19. 
    Weak positivity and the stability of certain Hilbert points. Inventiones math. 96 (1989) 639 - 667
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20. 
    (with H. Esnault) Effective bounds for semipositive sheaves and the height of points on curves over complexe function fields. Compositio math. 76 (1990) 69 - 85
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21. 
    Weak positivity and the stability of certain Hilbert points II. Inventiones math. 101 (1990) 191 - 223
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22. 
    Weak positivity and the stability of certain Hilbert points III. Inventiones math. 101 (1990) 521 - 543
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23. 
    Quasi-projective quotients by compact equivalence relations. Math. Ann. 289, (1991) 297 - 314
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24. 
    (with H. Esnault) Ample sheaves on moduli schemes. ``Proceedings of the Conference in Algebraic and Analytic Geometry'', Tokyo, 1990, ICM-90 Satellite Conference Proceedings, Springer , 53-81
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25. 
    (with H. Esnault and J. Seade) Characteristic divisors on complex manifolds. Journ. reine angew. Math. 424 (1992) 17-30
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26. 
    (with H. Esnault and V. Schechtman) Cohomology of local systems on the complement of hyperplanes. Invent. math. 109 (1992) 557-561
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    Erratum: Invent. math. 112 (1993) 447
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27. 
    (with H. Esnault and B. Kahn) Coverings with odd ramification and Stiefel-Withney classes. Journ. f. reine und ang. Math. 441 (1993) 145-188
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28. 
    (with H. Esnault) Higher Kodaira-Spencer classes. Math. Ann. 299 (1994) 491-527
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29. 
    (with H. Esnault and V. Srinivas) Decomposability of Chow groups implies decomposability of cohomology. ``Journées de Géométrie Algébrique d'Orsay, Juillet 1992'', Astérisque 218 (1993) 227 - 242
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30. 
    (with H. Esnault and M. Levine) Chow groups on projective varieties of very small degree. Duke Math. J. 87 (1997), 29-58
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31. 
    (with H. Esnault, B. Kahn and M. Levine) The Arason invariant and mod 2 algebraic cycles. Journal of the American Mathematical Society 11 (1998), 73-118
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32. 
    (with H. Esnault and V. Srinivas) The universal regular quotient of the Chow group of 0-cycles on a singular projective variety. Inventiones math. 135 (1999) 595-664
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33. 
    (with H. Esnault) Germs of de Rham cohomology classes which vanish at the generic point. CRAS, Paris 326 (1998), 857-862
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34. 
    (with Sheng-Li Tan) A note on Cayley-Bacharach property for vector bundles. In: Complex Analysis and Algebraic Geometry (2000) 361 - 373, Walter de Gruyter, Berlin-New York.
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35. 
    (with H. Esnault) Semistable bundles on curves and irreducible representations of the fundamental group. Contemporary Mathematics 241 (1999) 129 - 138
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36. 
    (with E. Bedulev) On the Shafarevich conjecture for surfaces of general type over function fields. Invent. Math. 139 (2000) 603-615
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37. 
    (with K. Oguiso) On the isotriviality of families of elliptic surfaces. J. Alg. Geom. 10 (2001) 569-598
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38. 
    (with K. Zuo) On the isotriviality of families of projective manifolds over curves. J. Alg. Geom. 10 (2001) 781-799
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39. 
    (with K. Zuo) On the Brody hyperbolicity of moduli spaces for canonically polarized manifolds. Duke Math. Journal 118 (2003) 103-150
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40. 
    (with K. Zuo) Base spaces of non-isotrivial families of smooth minimal models. In Complex Geometry (Grauert Festschrift) Springer Verlag 2002, 279-328
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41. 
    (with H. Esnault) Chern classes of Gauß-Manin bundles of weight 1 vanish. K-theory 26 (2002) 287-305
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42. 
    (with K. Zuo) Families of abelian varieties over curves with maximal Higgs field. J. Diff. Geom. 66 (2004) 233-287.
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    and an example which did not make it to the published version.
    (an earlier version of the first part was:
    Families of abelian varieties over curves with maximal Higgs field. preprint 2002, 14 pages)
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43. 
    (with K. Zuo) Discreteness of minimal models of Kodaira dimension zero and subvarieties of moduli stacks. Survey in differential geometry VIII 337-356, Edited by S.-T. Yau, International Press, 2004
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44. 
    (with M. Chen) Bicanonical and adjoint linear systems on surfaces of general type. Pacific J. of Math. 219 (2005) 83-96
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    Corrections, pdf     Corrections, (LaTeX-source)
45. 
    (with K. Zuo) Families over curves with a strictly maximal Higgs field. Asian J. of Math. 7 (2003) 575 - 598
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46. 
    (with J.-X. Cai) Irregular manifolds whose canonical system is composed with a pencil. Asian J. of Math. 8 (2004) 27-38
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47. 
    (with K. Zuo) Complex multiplication, Griffiths-Yukawa couplings, and rigidy for families of hypersurfaces. J. Alg. Geom. 14 (2005) 481-528
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48. 
    (with K. Zuo) Geometry and arithmetic of non-rigid families of Calabi-Yau 3-folds; questions and examples. AMS/IP Studies in Advanced Mathematics (Mirror Symmetry V). 38 (2006) 351-360.
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49. 
    (with K. Zuo) Arakelov inequalities and the uniformization of certain rigid Shimura varieties. J. Diff. Geom. 77 (2007) 291-352
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50. 
    (with K. Zuo) Numerical bounds for semi-stable families of curves or of certain higher dimensional manifolds. J. Alg. Geom. 15 (2006) 771--791
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51. 
    (with K. Zuo) Special subvarieties of A_g. Proc. of the ICCM 2004. AMS Studies in Advanced Mathematics. 42 (2008) 111-124
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52. 
    (with M. Möller, K. Zuo) Special families of curves, of Abelian varieties, and of certain minimal manifolds over curves. In: Global Aspects of Complex Geometry. Springer Verlag 2006, pp. 417--450.
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53. 
    Compactifications of smooth families and of moduli spaces of polarized manifold. Annals of Mathematics 172 (2010), 809--910.
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54. 
    (with M. Möller, K. Zuo) Stability of Hodge bundles and a numerical characterization of Shimura varieties, arxiv:0706.3462, Journ. Diff. Geom. 92 (2012), 71-151.
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55. 
    (with D.-Q. Zhang) Effective Iitaka fibrations, J. Alg. Geom. 18 (2009) 711-730
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56. 
    (with S. Müller-Stach, K. Zuo) Relative Proportionality for subvarieties of moduli spaces of K3 and abelian surfaces. Pure Appl. Math. Quarterly 5 (Special Issue: In honor of Friedrich Hirzebruch, Part 2, 2009) 1161-1199
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57. 
    (with M. Möller) Kobayashi geodesics in A_g, Journal of Diff. Geom 86 Nr. 2 (2011), 355-379
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58. 
    (with J.-M. Hwang) Characteristic foliation on a hypersurface of general type in a projective symplectic manifold, Compositio Math. 146 (2) (2010), 497--506.
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59. 
    Arakelov (in)equalities. Survey in differential geometry XIII 245 - 275.
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60. 
    (with H. Esnault) On a rationality question in the Grothendieck ring of varieties. Acta Mathematica Vietnamica 35, (2010), 31-41.
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61. 
    (with H. Esnault) Surface singularities dominated by smooth varieties, Journ. reine angew. Math. 649 (2010), 1--9.
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Announcements and survey articles (not refereed):
1. Classification theory of algebraic threefolds. Rend. Sem. Mat. Univers. Politcn. Torino 37 (1979) 11 - 16
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2. 
   Zur Klassifikationstheorie drei (und höher) dimensionaler projektiver Mannigfaltigkeiten. Jahresber. DMV 86 (1984) 135 - 150
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3. 
   Vanishing theorems and positivity in algebraic fibre spaces. Proc. ICM, Berkeley 1986 (Inv. Address, Sect 06), 682 - 688
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4. 
   Positivity of sheaves and geometric invariant theory. in: Proc. of the ''A.I. Maltsev Conf.'' on Algebra and Analysis. Novosibirsk 1989. Contemporary Math. 131 (1992) 499 - 513
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5. 
   Survey on quasi-projective moduli of polarized manifolds. Material for a series of talks at the ICTP, Trieste, 1994, 19 pages
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6. 
   Commentary on D. Mumford's paper on ``The classification of surfaces and other varieties''. Appendix to D. Mumford's Selected Papers. 647-660, Springer Verlag, 2004
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7. 
   Positivity of direct image sheaves and applications to families of higher dimensional manifolds. ICTP-Lecture Notes 6 (2001) 249-284
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Books:
1. (with H. Esnault) Lectures on Vanishing Theorems, Lecture Notes, Birkhäuser, DMV Seminar 20 (1992) 164 pages
   (LaTeX-source)     ps     ps.gz     pdf
2. 
   Quasi-Projective Moduli for Polarized Manifolds. Ergebnisse der Mathematik 30 (1995) Springer Verlag, 320 pages
   (LaTeX-source)     ps     ps.gz     pdf



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Notes of 2 seminar talks.



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