Eckart Viehweg, List of publications, 2008
Diplom:
- Die zahme Fundamentalgruppe einer ebenen Quartic
mit drei Spitzen, Heidelberg 1972.
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Dissertation:
- Invarianten der degenerierten Fasern in lokalen Familien von
Kurven, Mannheim 1975.
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Articles:
- 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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Rational singularities of higher dimensional schemes.
Proc. AMS 63 (1977) 6 - 8
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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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Klassifikationstheorie algebraischer Varietäten der Dimension drei,
Compositio math. 41 (1980) 361 - 400 (Habilitation, Mannheim, 1980)
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(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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Die Additivität der Kodaira Dimension für projektive Faserräume
über Varietäten des allgemeinen Typs.
Journ. reine angew. Math. 330 (1982) 132 - 142
pdf
Vanishing theorems. Journ. reine angew. Math. 335 (1982) 1 - 8
pdf
(with H. Esnault) Revêtement cycliques. Algebraic Threefolds,
Proc. Varenna 1981. Springer Lect. Notes in Math. 947, 241 - 250
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(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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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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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
(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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(with H. Esnault) Two dimensional quotient singularities deform to
quotient singularities. Math. Ann 271 (1985) 439 - 449
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(with H. Esnault) Revêtements cycliques II, Proc. Algebraic Geometry,
La Rabida 1984, Hermann, Travaux en cours 23 (1987) 81 - 96
pdf
(with H. Esnault) Logarithmic De Rham complexes and vanishing theorems.
Inventiones math. 86 (1986) 161 - 194
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(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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(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
(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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Weak positivity and the stability of certain Hilbert points.
Inventiones math. 96 (1989) 639 - 667
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(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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Weak positivity and the stability of certain Hilbert points II.
Inventiones math. 101 (1990) 191 - 223
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Weak positivity and the stability of certain Hilbert points III.
Inventiones math. 101 (1990) 521 - 543
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Quasi-projective quotients by compact equivalence relations. Math. Ann.
289, (1991) 297 - 314
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(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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(with H. Esnault and J. Seade) Characteristic divisors on complex
manifolds.
Journ. reine angew. Math. 424 (1992) 17-30
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(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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(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
(with H. Esnault) Higher Kodaira-Spencer classes.
Math. Ann. 299 (1994) 491-527
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(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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(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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(LaTeX-source)
(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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(LaTeX-source)
(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)
(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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(LaTeX-source)
(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)
(with H. Esnault) Semistable bundles on curves and
irreducible representations of the fundamental group.
Contemporary Mathematics 241 (1999) 129 - 138
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(LaTeX-source)
(with E. Bedulev) On the Shafarevich
conjecture for surfaces of general type over function fields.
Invent. Math. 139 (2000) 603-615
pdf
(LaTeX-source)
(with K. Oguiso) On the isotriviality of
families of elliptic surfaces. J. Alg. Geom. 10 (2001) 569-598
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(LaTeX-source)
(with K. Zuo) On the isotriviality of families
of projective manifolds over curves. J. Alg. Geom. 10 (2001) 781-799
pdf
(LaTeX-source)
(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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(LaTeX-source)
(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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(LaTeX-source)
(with H. Esnault) Chern classes of Gauß-Manin bundles
of weight 1 vanish. K-theory 26 (2002) 287-305
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(LaTeX-source)
(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)
(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)
(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)
(with K. Zuo) Families over curves
with a strictly maximal Higgs field.
Asian J. of Math. 7 (2003) 575 - 598
pdf
(LaTeX-source)
(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)
(with K. Zuo) Complex multiplication, Griffiths-Yukawa couplings, and rigidy for
families of hypersurfaces. J. Alg. Geom. 14 (2005) 481-528
pdf
(LaTeX-source)
(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)
(with K. Zuo) Arakelov inequalities and the uniformization of certain rigid Shimura varieties. J. Diff. Geom. 77 (2007) 291-352
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(LaTeX-source)
(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)
(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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(LaTeX-source)
(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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(LaTeX-source)
Compactifications of smooth families
and of moduli spaces of polarized manifold. Annals of Mathematics 172 (2010), 809--910.
pdf
(LaTeX-source)
(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)
(with D.-Q. Zhang)
Effective Iitaka fibrations, J. Alg. Geom. 18 (2009) 711-730
pdf
(LaTeX-source)
(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)
(with M. Möller)
Kobayashi geodesics in A_g,
Journal of Diff. Geom 86 Nr. 2 (2011), 355-379
pdf
(LaTeX-source)
(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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Arakelov (in)equalities. Survey in differential geometry XIII
245 - 275.
pdf
(LaTeX-source)
(with H. Esnault)
On a rationality question in the Grothendieck ring of varieties. Acta Mathematica Vietnamica
35, (2010), 31-41.
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(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):
- Classification theory of algebraic threefolds. Rend. Sem. Mat.
Univers. Politcn. Torino 37 (1979) 11 - 16
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Zur Klassifikationstheorie drei (und höher) dimensionaler projektiver
Mannigfaltigkeiten. Jahresber. DMV 86 (1984) 135 - 150
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Vanishing theorems and positivity in algebraic fibre spaces.
Proc. ICM, Berkeley 1986 (Inv. Address, Sect 06), 682 - 688
pdf
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
Survey on quasi-projective moduli of polarized manifolds.
Material for a series of talks at the ICTP, Trieste, 1994, 19 pages
pdf
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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Positivity of direct image sheaves and applications to
families of higher dimensional manifolds. ICTP-Lecture Notes 6 (2001)
249-284
pdf
(LaTeX-source)
Books:
- (with H. Esnault) Lectures on Vanishing Theorems, Lecture Notes,
Birkhäuser, DMV Seminar 20 (1992) 164 pages
(LaTeX-source)
ps
ps.gz
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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.
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