Brill–Noether theory for curves on generic abelian surfaces

Bayer, Arend; Li, Chunyi

doi:10.4310/pamq.2017.v13.n1.a2

Cited by 12 publications

(8 citation statements)

References 8 publications

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“…In particular there are curves carrying linear series with negative Brill-Noether number and they can prove under certain hypothesis on the Brill-Noether number that these Brill-Noether loci are of the expected codimension in |H|. A similar result was obtained before with different techniques by Paris [21] and generalized by Bayer and Li [6].…”

Section: Introductionsupporting

confidence: 70%

Brill-Noether theory and Green's conjecture for general curves on simple abelian surfaces

Moretti¹

2022

Preprint

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Section: Introductionsupporting

confidence: 70%

Brill-Noether theory and Green's conjecture for general curves on simple abelian surfaces

Moretti¹

2022

Preprint

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“…In this case F is torsion, but the same analysis works as in the torsion-free case thanks to [BL17]. Then, as explained in [JP20, Example 4.3] the function h 0 F,L is trivial; according to Proposition 7.1, it follows that F is semistable on the whole (α, β)-plane.…”

Section: Chern Degree Functions Of Gieseker Semistable Sheavesmentioning

confidence: 81%

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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“…In fact, more is true: there is a nonempty distinguished component of the space of Bridgeland stability conditions on , such that, for generic with respect to , the moduli space of -stable objects in of class is nonempty of dimension . For a K3 surface this is [BM14b, Theorem 6.8] and [BM14a, Theorem 2.15] (based on [Yos01, Yos06]), and for an abelian surface and this is [BL17, Theorem 2.3] (based on [Yos16, MYY14]), but the case of general holds by similar arguments. This completes the proof, because a Bridgeland stable object is necessarily simple and universally gluable.…”

Section: Proofs Of Results On the Integral Hodge Conjecturementioning

confidence: 99%

The integral Hodge conjecture for two-dimensional Calabi–Yau categories

Perry¹

2022

Compositio Math.

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We formulate a version of the integral Hodge conjecture for categories, prove the conjecture for two-dimensional Calabi–Yau categories which are suitably deformation equivalent to the derived category of a K3 or abelian surface, and use this to deduce cases of the usual integral Hodge conjecture for varieties. Along the way, we prove a version of the variational integral Hodge conjecture for families of two-dimensional Calabi–Yau categories, as well as a general smoothness result for relative moduli spaces of objects in such families. Our machinery also has applications to the structure of intermediate Jacobians, such as a criterion in terms of derived categories for when they split as a sum of Jacobians of curves.

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Brill–Noether theory for curves on generic abelian surfaces

Cited by 12 publications

References 8 publications

Brill-Noether theory and Green's conjecture for general curves on simple abelian surfaces

Brill-Noether theory and Green's conjecture for general curves on simple abelian surfaces

Chern degree functions

The integral Hodge conjecture for two-dimensional Calabi–Yau categories

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