Virtual classes via vanishing cycles
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866910801838735360 |
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| author | Kinjo, Tasuki |
| author_facet | Kinjo, Tasuki |
| contents | We develop a new method to construct the virtual fundamental classes for quasi-smooth derived schemes using the perverse sheaves of vanishing cycles on their $-1$-shifted contangent spaces. It is based on the author's previous work that can be regarded as a version of the Thom isomorphism for $-1$-shifted cotangent spaces. We use the Fourier-Sato transform to prove that our classes coincide with the virtual fundamental classes introduced by the work of Behrend-Fantechi and Li-Tian, under the quasi-projectivity assumption. We also discuss an approach to construct DT4 virtual classes for $-2$-shifted symplectic derived schemes using the perverse sheaves of vanishing cycles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_06468 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Virtual classes via vanishing cycles Kinjo, Tasuki Algebraic Geometry We develop a new method to construct the virtual fundamental classes for quasi-smooth derived schemes using the perverse sheaves of vanishing cycles on their $-1$-shifted contangent spaces. It is based on the author's previous work that can be regarded as a version of the Thom isomorphism for $-1$-shifted cotangent spaces. We use the Fourier-Sato transform to prove that our classes coincide with the virtual fundamental classes introduced by the work of Behrend-Fantechi and Li-Tian, under the quasi-projectivity assumption. We also discuss an approach to construct DT4 virtual classes for $-2$-shifted symplectic derived schemes using the perverse sheaves of vanishing cycles. |
| title | Virtual classes via vanishing cycles |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2109.06468 |