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arXiv · 2403.12855

Uniform boundedness of semistable pure sheaves on projective manifolds

Mihai Pavel·Julius Ross·Matei Toma
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Abstract

We prove uniform boundedness statements for semistable pure sheaves on projective manifolds. For example, we prove that the set of isomorphism classes of pure sheaves of dimension 2 that are slope semistable with respect to ample classes that vary in a compact set $K$ are bounded. We also prove uniform boundedness for pure sheaves of higher dimension, but with restrictions on the compact set $K$. As applications we get new statements about moduli spaces of semistable sheaves, and the wall-chamber structure that governs their variation.

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Mihai Pavel, Julius Ross, Matei Toma. 2024-03-19. Uniform boundedness of semistable pure sheaves on projective manifolds. https://arxiv.org/abs/2403.12855

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