Syzygies of abelian varieties

DOI10.1090/S0894-0347-00-00335-0zbMath0956.14035MaRDI QIDQ4955890

Giuseppe Pareschi

Publication date: 22 May 2000

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

syzygieshomogeneous idealample line bundle on an abelian variety

Mathematics Subject Classification ID

Related Items (26)

Regularity on abelian varieties I ⋮ Syzygies of some GIT quotients ⋮ Projective normality of abelian varieties ⋮ On irregular threefolds and fourfolds with numerically trivial canonical bundle ⋮ Resolutions of Segre embeddings of projective spaces of any dimension ⋮ New constructions of nef classes on self-products of curves ⋮ M-regularity of ℚ-twisted sheaves and its application to linear systems on abelian varieties ⋮ Asymptotic vanishing of syzygies of algebraic varieties ⋮ Syzygies of Kummer varieties ⋮ Continuous CM-regularity and generic vanishing. With an appendix by Atsushi Ito (Okayama University) ⋮ On syzygies of Calabi-Yau varieties and varieties of general type ⋮ Local positivity, multiplier ideals, and syzygies of abelian varieties ⋮ On syzygies of projective bundles over abelian varieties ⋮ A remark on higher syzygies on abelian surfaces ⋮ Torsion points on theta divisors and semihomogeneous vector bundles ⋮ Index conditions and cup-product maps on Abelian varieties ⋮ Asymptotic syzygies of algebraic varieties ⋮ Verlinde bundles and generalized theta linear series ⋮ On the vanishing of weight one Koszul cohomology of abelian varieties ⋮ Embedding theorems on hyperelliptic varieties ⋮ Regularity on abelian varieties II: Basic results on linear series and defining equations ⋮ The basepoint-freeness threshold of a very general abelian surface ⋮ The basepoint-freeness threshold and syzygies of abelian varieties ⋮ On the projective normality and normal presentation on higher dimensional varieties with nef canonical bundle ⋮ Dimension estimates for Hilbert schemes and effective base point freeness on moduli spaces of vector bundles on curves. ⋮ Rank 3 quadratic generators of Veronese embeddings

Cites Work

• Koszul cohomology and the geometry of projective varieties. Appendix: The nonvanishing of certain Koszul cohomology groups (by Mark Green and Robert Lazarsfeld)
• Complex abelian varieties and theta functions
• Syzygies and Koszul cohomology of smooth projective varieties of arbitrary dimension
• On the normal generation by a line bundle on an Abelian variety
• On the equations defining Abelian varieties. I-III
• Duality between D(X) and with its application to picard sheaves
• Linear Systems on Abelian Varieties
• Toward the Inversion of Abelian Integrals, II
• Theta Relations and Projective Normality of Abelian Varieties
• Multiplication Over Abelian Varieties
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