Tilt-stability, vanishing theorems and Bogomolov-Gieseker type inequalities

Sun, Hao

doi:10.1016/j.aim.2019.02.026

Cited by 6 publications

(1 citation statement)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Applications and open questions. Bogomolov's inequality has many interesting applications, such as the the positivity of adjoint linear systems (see [25,3]), and vanishing theorems for semistable sheaves (see [29]). By Theorem 1.3, all these related results automatically hold for product type surfaces in positive characteristic (see Theorem 6.1 and 6.2).…”

mentioning

confidence: 99%

Bogomolov's inequality for product type varieties in positive characteristic

Sun¹

2019

Preprint

View full text Add to dashboard Cite

We prove Bogomolov's inequality for semistable sheaves on product type varieties in arbitrary characteristic. This gives the first examples of varieties with positive Kodaira dimension in positive characteristic on which Bogomolov's inequality holds for semistable sheaves of any rank. The key ingredient in the proof is a high rank generalization of the slope inequality established by Xiao and Cornalba-Harris. This Bogomolov's inequality is applied to study the positivity of linear systems and semistable sheaves and construct Bridgeland stability conditions on product type surfaces in positive characteristic. We also give some new counterexamples to Bogomolov's inequality and pose some open questions. Contents 14 7. Counterexamples to Bogomolov's inequality 16 References 17

show abstract

mentioning

confidence: 99%

Bogomolov's inequality for product type varieties in positive characteristic

Sun¹

2019

Preprint

View full text Add to dashboard Cite

show abstract

An effective restriction theorem via wall-crossing and Mercat’s conjecture

Feyzbakhsh

2022

Math. Z.

View full text Add to dashboard Cite

We prove an effective restriction theorem for stable vector bundles E on a smooth projective variety: $$E|_D$$ E | D is (semi)stable for all irreducible divisors $$D \in |kH|$$ D ∈ | k H | for all k greater than an explicit constant. As an application, we show that Mercat’s conjecture in any rank greater than 2 fails for curves lying on K3 surfaces. Our technique is to use wall-crossing with respect to (weak) Bridgeland stability conditions which we also use to reprove Camere’s result on slope stability of the tangent bundle of $${\mathbb {P}}^n$$ P n restricted to a K3 surface.

show abstract

Cohomology bounds and Chern class inequalities for stable sheaves on a smooth projective variety

Nakashima

2022

Indian J Pure Appl Math

View full text Add to dashboard Cite

Tilt-stability, vanishing theorems and Bogomolov-Gieseker type inequalities

Cited by 6 publications

References 39 publications

Bogomolov's inequality for product type varieties in positive characteristic

Bogomolov's inequality for product type varieties in positive characteristic

An effective restriction theorem via wall-crossing and Mercat’s conjecture

Cohomology bounds and Chern class inequalities for stable sheaves on a smooth projective variety

Contact Info

Product

Resources

About