Uniform boundedness of semistable pure sheaves on projective manifolds
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911803596865536 |
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| author | Pavel, Mihai Ross, Julius Toma, Matei |
| author_facet | Pavel, Mihai Ross, Julius Toma, Matei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_12855 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniform boundedness of semistable pure sheaves on projective manifolds Pavel, Mihai Ross, Julius Toma, Matei Algebraic Geometry 14D20, 32G13 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. |
| title | Uniform boundedness of semistable pure sheaves on projective manifolds |
| topic | Algebraic Geometry 14D20, 32G13 |
| url | https://arxiv.org/abs/2403.12855 |