Welcome to the University, Duisburg-Essen Welcome to the SFB-TR 45Universität Duisburg-Essen

Mathematik, Campus Essen


Eckart Viehweg, List of publications, 2008


    Diplom:
    1. Die zahme Fundamentalgruppe einer ebenen Quartic mit drei Spitzen, Heidelberg 1972.
      pdf

    Dissertation:
    1. Invarianten der degenerierten Fasern in lokalen Familien von Kurven, Mannheim 1975.
      pdf


    Articles:
    1. Invarianten der degenerierten Fasern in lokalen Familien von Kurven. Journ. reine angew. Math. 293/294 (1977) 284 - 308 (Résumé of the thesis)
      pdf

    2. Rational singularities of higher dimensional schemes. Proc. AMS 63 (1977) 6 - 8
      pdf

    3. Canonical divisors and the additivity of the Kodaira dimension for morphisms of relative dimension one. Compositio Math. 35 (1977) 197 - 223
      pdf
      Erratum: Compositio Math. 35 (1977) 336
      pdf

    4. Klassifikationstheorie algebraischer Varietäten der Dimension drei, Compositio math. 41 (1980) 361 - 400 (Habilitation, Mannheim, 1980)
      pdf

    5. (with Y. Kawamata) On a characterization of an abelian variety in the classification theory of algebraic varieties. Compositio math. 41 (1980) 355 - 359
      pdf

    6. Die Additivität der Kodaira Dimension für projektive Faserräume über Varietäten des allgemeinen Typs. Journ. reine angew. Math. 330 (1982) 132 - 142
      pdf

    7. Vanishing theorems. Journ. reine angew. Math. 335 (1982) 1 - 8
      pdf

    8. (with H. Esnault) Revêtement cycliques. Algebraic Threefolds, Proc. Varenna 1981. Springer Lect. Notes in Math. 947, 241 - 250
      pdf

    9. (with H. Esnault) Sur une minoration du degré d'hypersurfaces s'annulant en certains points. Math. Ann. 263 (1983) 75 - 86
      pdf

    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
      pdf

    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
      pdf

    12. (with H. Esnault) Dyson's lemma for polynomials in several variables (and the theorem of Roth). Inventiones math. 78 (1984) 445 - 490
      pdf

    13. (with H. Esnault) Two dimensional quotient singularities deform to quotient singularities. Math. Ann 271 (1985) 439 - 449
      pdf

    14. (with H. Esnault) Revêtements cycliques II, Proc. Algebraic Geometry, La Rabida 1984, Hermann, Travaux en cours 23 (1987) 81 - 96
      pdf

    15. (with H. Esnault) Logarithmic De Rham complexes and vanishing theorems. Inventiones math. 86 (1986) 161 - 194
      pdf

    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
      pdf

    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
      pdf

    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
      pdf

    19. Weak positivity and the stability of certain Hilbert points. Inventiones math. 96 (1989) 639 - 667
      pdf

    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
      pdf

    21. Weak positivity and the stability of certain Hilbert points II. Inventiones math. 101 (1990) 191 - 223
      pdf

    22. Weak positivity and the stability of certain Hilbert points III. Inventiones math. 101 (1990) 521 - 543
      pdf

    23. Quasi-projective quotients by compact equivalence relations. Math. Ann. 289, (1991) 297 - 314
      pdf

    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
      pdf

    25. (with H. Esnault and J. Seade) Characteristic divisors on complex manifolds. Journ. reine angew. Math. 424 (1992) 17-30
      pdf

    26. (with H. Esnault and V. Schechtman) Cohomology of local systems on the complement of hyperplanes. Invent. math. 109 (1992) 557-561
      pdf
      Erratum: Invent. math. 112 (1993) 447
      pdf

    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
      pdf

    28. (with H. Esnault) Higher Kodaira-Spencer classes. Math. Ann. 299 (1994) 491-527
      pdf

    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
      pdf

    30. (with H. Esnault and M. Levine) Chow groups on projective varieties of very small degree. Duke Math. J. 87 (1997), 29-58
      pdf     (LaTeX-source)

    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
      pdf     (LaTeX-source)

    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
      pdf     (LaTeX-source)

    33. (with H. Esnault) Germs of de Rham cohomology classes which vanish at the generic point. CRAS, Paris 326 (1998), 857-862
      pdf     (LaTeX-source)

    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.
      pdf     (LaTeX-source)

    35. (with H. Esnault) Semistable bundles on curves and irreducible representations of the fundamental group. Contemporary Mathematics 241 (1999) 129 - 138
      pdf     (LaTeX-source)

    36. (with E. Bedulev) On the Shafarevich conjecture for surfaces of general type over function fields. Invent. Math. 139 (2000) 603-615
      pdf     (LaTeX-source)

    37. (with K. Oguiso) On the isotriviality of families of elliptic surfaces. J. Alg. Geom. 10 (2001) 569-598
      pdf     (LaTeX-source)

    38. (with K. Zuo) On the isotriviality of families of projective manifolds over curves. J. Alg. Geom. 10 (2001) 781-799
      pdf     (LaTeX-source)

    39. (with K. Zuo) On the Brody hyperbolicity of moduli spaces for canonically polarized manifolds. Duke Math. Journal 118 (2003) 103-150
      pdf     (LaTeX-source)

    40. (with K. Zuo) Base spaces of non-isotrivial families of smooth minimal models. In Complex Geometry (Grauert Festschrift) Springer Verlag 2002, 279-328
      pdf     (LaTeX-source)

    41. (with H. Esnault) Chern classes of Gauß-Manin bundles of weight 1 vanish. K-theory 26 (2002) 287-305
      pdf     (LaTeX-source)

    42. (with K. Zuo) Families of abelian varieties over curves with maximal Higgs field. J. Diff. Geom. 66 (2004) 233-287.
      pdf     (LaTeX-source)
      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)
      pdf     (LaTeX-source)

    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
      pdf     (LaTeX-source)

    44. (with M. Chen) Bicanonical and adjoint linear systems on surfaces of general type. Pacific J. of Math. 219 (2005) 83-96
      pdf     (LaTeX-source)
      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
      pdf     (LaTeX-source)

    46. (with J.-X. Cai) Irregular manifolds whose canonical system is composed with a pencil. Asian J. of Math. 8 (2004) 27-38
      pdf     (LaTeX-source)

    47. (with K. Zuo) Complex multiplication, Griffiths-Yukawa couplings, and rigidy for families of hypersurfaces. J. Alg. Geom. 14 (2005) 481-528
      pdf     (LaTeX-source)

    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.
      pdf     (LaTeX-source)

    49. (with K. Zuo) Arakelov inequalities and the uniformization of certain rigid Shimura varieties. J. Diff. Geom. 77 (2007) 291-352
      pdf     (LaTeX-source)

    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
      pdf     (LaTeX-source)

    51. (with K. Zuo) Special subvarieties of A_g. Proc. of the ICCM 2004. AMS Studies in Advanced Mathematics. 42 (2008) 111-124
      pdf     (LaTeX-source)

    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.
      pdf     (LaTeX-source)

    53. Compactifications of smooth families and of moduli spaces of polarized manifold. Annals of Mathematics 172 (2010), 809--910.
      pdf     (LaTeX-source)

    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.
      pdf     (LaTeX-source)

    55. (with D.-Q. Zhang) Effective Iitaka fibrations, J. Alg. Geom. 18 (2009) 711-730
      pdf     (LaTeX-source)

    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
      pdf     (LaTeX-source)

    57. (with M. Möller) Kobayashi geodesics in A_g, Journal of Diff. Geom 86 Nr. 2 (2011), 355-379
      pdf     (LaTeX-source)

    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.
      pdf

    59. Arakelov (in)equalities. Survey in differential geometry XIII 245 - 275.
      pdf     (LaTeX-source)

    60. (with H. Esnault) On a rationality question in the Grothendieck ring of varieties. Acta Mathematica Vietnamica 35, (2010), 31-41.
      pdf

    61. (with H. Esnault) Surface singularities dominated by smooth varieties, Journ. reine angew. Math. 649 (2010), 1--9.
      pdf

    Announcements and survey articles (not refereed):
    1. Classification theory of algebraic threefolds. Rend. Sem. Mat. Univers. Politcn. Torino 37 (1979) 11 - 16
      pdf

    2. Zur Klassifikationstheorie drei (und höher) dimensionaler projektiver Mannigfaltigkeiten. Jahresber. DMV 86 (1984) 135 - 150
      pdf

    3. Vanishing theorems and positivity in algebraic fibre spaces. Proc. ICM, Berkeley 1986 (Inv. Address, Sect 06), 682 - 688
      pdf

    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
      pdf

    5. Survey on quasi-projective moduli of polarized manifolds. Material for a series of talks at the ICTP, Trieste, 1994, 19 pages
      pdf

    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
      pdf

    7. Positivity of direct image sheaves and applications to families of higher dimensional manifolds. ICTP-Lecture Notes 6 (2001) 249-284
      pdf     (LaTeX-source)

    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


    Notes of 2 seminar talks.


    Back to the main page of our research group.

    Comments and questions: Webmaster

    Valid HTML 4.01!