Cohomological rank functions and Syzygies of abelian varieties

Jiang, Zhi

doi:10.48550/arxiv.2010.10053

Cited by 4 publications

(4 citation statements)

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“…To show (N p ), Theorem 1.4 is also used in [Ito20], [Jia20], where techniques to cutting minimal log canonical centers are used to bound β(l) from above. In this paper we do not need such techniques.…”

Section: Introductionmentioning

confidence: 99%

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Higher syzygies on general polarized abelian varieties of type $(1,\dots,1,d)$

Ito¹

2020

Preprint

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Section: Introductionmentioning

confidence: 99%

“…Acknowledgments. The author would like to express his gratitude to Professor Zhi Jiang for sending drafts of [Jia20] to the author. He also thanks Professor Victor Lozovanu for valuable comments.…”

Section: Introductionmentioning

confidence: 99%

Higher syzygies on general polarized abelian varieties of type $(1,\dots,1,d)$

Ito¹

2020

Preprint

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“…geographical lower bounds of the volume of a line bundle and characterize the polarized varieties where the bound is attained ( [BPS20a,Jia21]). They have been also applied to the study of syzygies of abelian varieties (see [Cau20,Jia20,Ito20] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Chern degree functions

Lahoz,

Rojas

2021

Preprint

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We introduce Chern degree functions for complexes of coherent sheaves on a polarized surface, which encode information given by stability conditions on the boundary of the (α, β)-plane. We prove that these functions extend to continuous real valued functions and we study their differentiability in terms of stability. For abelian surfaces, Chern degree functions coincide with the cohomological rank functions defined by Jiang-Pareschi. We illustrate in some geometrical situations a general strategy to compute these functions.

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“…Caucci's result has received considerable attention as an effective tool to understand the syzygies of abelian varieties endowed with a primitive polarization (i.e. a polarization which is not a multiple of another one), by means of upper bounds for the basepoint-freeness threshold (see [Jia20,Ito20a,Ito20b]). Furthermore, for p ≥ 1 the hypothesis ǫ 1 (l) < 1 p+2 ensuring (N p ) has recently been slightly weakened by Ito ([Ito21, Theorem 1.5]).…”

Section: Introductionmentioning

confidence: 99%

The basepoint-freeness threshold of a very general abelian surface

Rojas¹

2021

Preprint

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For abelian surfaces of Picard rank 1, we perform explicit computations of the cohomological rank functions of the ideal sheaf of one point, and in particular of the basepointfreeness threshold. Our main tool is the relation between cohomological rank functions and Bridgeland stability. In virtue of recent results of Caucci and Ito, these computations provide new information on the syzygies of polarized abelian surfaces.

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Cohomological rank functions and Syzygies of abelian varieties

Cited by 4 publications

References 12 publications

Higher syzygies on general polarized abelian varieties of type $(1,\dots,1,d)$

Higher syzygies on general polarized abelian varieties of type $(1,\dots,1,d)$

Chern degree functions

The basepoint-freeness threshold of a very general abelian surface

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