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

Soheyla Feyzbakhsh

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arXiv · 1608.07825

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

Soheyla Feyzbakhsh

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Abstract

We prove an effective restriction theorem for stable vector bundles $E$ on a smooth projective variety: $E|_D$ is (semi)stable for all irreducible divisors $D \in |kH|$ 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 $\mathbb{P}^n$ restricted to a K3 surface.

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Soheyla Feyzbakhsh. 2016-08-28. An effective restriction theorem via wall-crossing and Mercat's conjecture. https://arxiv.org/abs/1608.07825

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