Deformations of morphisms of coherent sheaves
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910236092137472 |
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| author | Iacono, Donatella Lepri, Emma Martinengo, Elena |
| author_facet | Iacono, Donatella Lepri, Emma Martinengo, Elena |
| contents | We generalise Hinich's Theorem of descent of Deligne groupoids to the case where the dgLas involved have no negative cohomology. We apply this result to study the infinitesimal deformations of a morphism $α: {\mathcal F} \to {\mathcal G}$ of coherent sheaves, where both the sheaves $ {\mathcal F}$ and $ {\mathcal G}$ and the map $α$ can be deformed, on a smooth variety over a field of characteristic zero. In particular, we provide an explicit dgLa that controls these deformations via the Deligne functor, applying the Thom-Whitney totalisation to a specific semicosimplicial dgLa, constructed from geometrical data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_19616 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Deformations of morphisms of coherent sheaves Iacono, Donatella Lepri, Emma Martinengo, Elena Algebraic Geometry 14B10, 14B12, 14D15, 13D10, 18F20 We generalise Hinich's Theorem of descent of Deligne groupoids to the case where the dgLas involved have no negative cohomology. We apply this result to study the infinitesimal deformations of a morphism $α: {\mathcal F} \to {\mathcal G}$ of coherent sheaves, where both the sheaves $ {\mathcal F}$ and $ {\mathcal G}$ and the map $α$ can be deformed, on a smooth variety over a field of characteristic zero. In particular, we provide an explicit dgLa that controls these deformations via the Deligne functor, applying the Thom-Whitney totalisation to a specific semicosimplicial dgLa, constructed from geometrical data. |
| title | Deformations of morphisms of coherent sheaves |
| topic | Algebraic Geometry 14B10, 14B12, 14D15, 13D10, 18F20 |
| url | https://arxiv.org/abs/2605.19616 |