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arXiv · 1107.0877

On the behaviour of strong semistability in geometric deformations

Holger Brenner·Axel Stäbler
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Abstract

Let $Y \to B$ be a relative smooth projective curve over an affine integral base scheme $B$ of positive characteristic. We provide for all prime characteristics example classes of vector bundles $\mathcal{S}$ over $Y$ such that $\mathcal{S}$ is generically strongly semistable and semistable but not strongly semistable for some special fibre. This also provides new examples of the behaviour of Hilbert-Kunz multiplicities in geometric families.

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Holger Brenner, Axel Stäbler. 2011-07-05. On the behaviour of strong semistability in geometric deformations. https://arxiv.org/abs/1107.0877

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