Chern degree functions

Lahoz, Martí; Rojas, Andrés

doi:10.1142/s0219199722500079

Cited by 3 publications

(2 citation statements)

References 33 publications

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“…Suppose , then we have This implies If , we have And thus, we get the curve . So we see that, if an object is -semistable for some generic , we have For a more detailed explanation of , we would like to ask readers to consult [LR22, FLZ22] on Le Potier functions.…”

Section: Introduction To Bridgeland Stabilitymentioning

confidence: 99%

Stability condition on Calabi–Yau threefold of complete intersection of quadratic and quartic hypersurfaces

Liu

2022

Forum of Mathematics, Sigma

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In this paper, we prove a Clifford type inequality for the curve $X_{2,2,2,4}$ , which is the intersection of a quartic and three general quadratics in $\mathbb {P}^5$ . We thus prove a stronger Bogomolov–Gieseker inequality for characters of stable vector bundles and stable objects on Calabi–Yau complete intersection $X_{2,4}$ . Applying the scheme proposed by Bayer, Bertram, Macrì, Stellari and Toda, we can construct an open subset of Bridgeland stability conditions on $X_{2,4}$ .

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Section: Introduction To Bridgeland Stabilitymentioning

confidence: 99%

Stability condition on Calabi–Yau threefold of complete intersection of quadratic and quartic hypersurfaces

Liu

2022

Forum of Mathematics, Sigma

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“…Based on Bridgeland’s stability condition on surfaces, Lahoz-Rojas [LR] and Rojas [R] almost determined the cohomological rank functions for any polarized abelian surface of Picard number . When L is of polarization type , Rojas proved that when d is a perfect square or where is the minimal or the second minimal positive solution of the Pell’s equation when d is not a perfect square.…”

Section: Introductionmentioning

confidence: 99%

Angehrn-Siu-Helmke’s method applied to abelian varieties

Jiang

2023

Forum of Mathematics, Sigma

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We apply Angehrn-Siu-Helmke’s method to estimate basepoint freeness thresholds of higher dimensional polarized abelian varieties. We showed that a conjecture of Caucci holds for very general polarized abelian varieties in the moduli spaces $\mathcal {A}_{g, l}$ with only finitely many possible exceptions of primitive polarization types l in each dimension g. We improved the bound of basepoint freeness thresholds of any polarized abelian $4$ -folds and simple abelian $5$ -folds.

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Stability manifolds of varieties with finite Albanese morphisms

Fu¹,

Li²,

Zhao³

2022

Trans. Amer. Math. Soc.

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For a smooth projective complex variety whose Albanese morphism is finite, we show that every Bridgeland stability condition on its bounded derived category of coherent sheaves is geometric, in the sense that all skyscraper sheaves are stable with the same phase. Furthermore, we describe the stability manifolds of irregular surfaces and abelian threefolds with Néron-Severi rank one, and show that they are connected and contractible. CONTENTS 1. Introduction 1 2. Geometric stability conditions 3 3. Surface case 9 4. Abelian threefold case 12 References 22

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Chern degree functions

Cited by 3 publications

References 33 publications

Stability condition on Calabi–Yau threefold of complete intersection of quadratic and quartic hypersurfaces

Stability condition on Calabi–Yau threefold of complete intersection of quadratic and quartic hypersurfaces

Angehrn-Siu-Helmke’s method applied to abelian varieties

Stability manifolds of varieties with finite Albanese morphisms

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