Intersection cohomology of moduli spaces of vector bundles over curves
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2015
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| _version_ | 1866912304072753152 |
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| author | Mozgovoy, Sergey Reineke, Markus |
| author_facet | Mozgovoy, Sergey Reineke, Markus |
| contents | We compute the intersection cohomology of the moduli spaces $M_{r,d}$ of semistable vector bundles having rank $r$ and degree $d$ over a curve. We do this by relating the Hodge-Deligne polynomial of the intersection cohomology of $M_{r,d}$ to the Donaldson-Thomas invariants of the curve. These invariants can be computed by methods going back to Harder, Narasimhan, Desale and Ramanan. More generally, we introduce Donaldson-Thomas classes in the Grothendieck group of mixed Hodge modules over $M_{r,d}$ and relate them to the class of the intersection complex of $M_{r,d}$. Our methods can be applied to the moduli spaces of semistable objects in arbitrary hereditary categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1512_04076 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | Intersection cohomology of moduli spaces of vector bundles over curves Mozgovoy, Sergey Reineke, Markus Algebraic Geometry We compute the intersection cohomology of the moduli spaces $M_{r,d}$ of semistable vector bundles having rank $r$ and degree $d$ over a curve. We do this by relating the Hodge-Deligne polynomial of the intersection cohomology of $M_{r,d}$ to the Donaldson-Thomas invariants of the curve. These invariants can be computed by methods going back to Harder, Narasimhan, Desale and Ramanan. More generally, we introduce Donaldson-Thomas classes in the Grothendieck group of mixed Hodge modules over $M_{r,d}$ and relate them to the class of the intersection complex of $M_{r,d}$. Our methods can be applied to the moduli spaces of semistable objects in arbitrary hereditary categories. |
| title | Intersection cohomology of moduli spaces of vector bundles over curves |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/1512.04076 |