A perfect obstruction theory for SU(2)-Higgs pairs
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866908321291698176 |
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| author | Schirren, Simon |
| author_facet | Schirren, Simon |
| contents | We present a new method for constructing virtual cycles for rank-2 Higgs sheaves $(E,ϕ)$ on a smooth projective surface $S$. Using this, we redefine the $\mathbf{SU}(2)$-perfect obstruction theory previously constructed by Tanaka-Thomas. The key step in our construction involves modifying the $\mathbf{C}^\times$-localisation formula of Graber-Pandharipande by replacing the torus action with an involution $(E,ϕ) \mapsto (E^*,-ϕ^*)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_16625 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A perfect obstruction theory for SU(2)-Higgs pairs Schirren, Simon Algebraic Geometry We present a new method for constructing virtual cycles for rank-2 Higgs sheaves $(E,ϕ)$ on a smooth projective surface $S$. Using this, we redefine the $\mathbf{SU}(2)$-perfect obstruction theory previously constructed by Tanaka-Thomas. The key step in our construction involves modifying the $\mathbf{C}^\times$-localisation formula of Graber-Pandharipande by replacing the torus action with an involution $(E,ϕ) \mapsto (E^*,-ϕ^*)$. |
| title | A perfect obstruction theory for SU(2)-Higgs pairs |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2403.16625 |