Exceptional collections on certain Hassett spaces
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866917640007581696 |
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| author | Castravet, Ana-Maria Tevelev, Jenia |
| author_facet | Castravet, Ana-Maria Tevelev, Jenia |
| contents | We construct an $S_2\times S_n$ invariant full exceptional collection on Hassett spaces of weighted stable rational curves with $n+2$ markings and weights $(\frac{1}{2}+η, \frac{1}{2}+η,ε,\ldots,ε)$, for $0<ε, η\ll1$ and can be identified with symmetric GIT quotients of $(\mathbb{P}^1)^n$ by the diagonal action of $\mathbb{G}_m$ when $n$ is odd, and their Kirwan desingularization when $n$ is even. The existence of such an exceptional collection is one of the needed ingredients in order to prove the existence of a full $S_n$-invariant exceptional collection on $\overline{\mathcal{M}}_{0,n}$. To prove exceptionality we use the method of windows in derived categories. To prove fullness we use previous work on the existence of invariant full exceptional collections on Losev-Manin spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2005_00751 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Exceptional collections on certain Hassett spaces Castravet, Ana-Maria Tevelev, Jenia Algebraic Geometry We construct an $S_2\times S_n$ invariant full exceptional collection on Hassett spaces of weighted stable rational curves with $n+2$ markings and weights $(\frac{1}{2}+η, \frac{1}{2}+η,ε,\ldots,ε)$, for $0<ε, η\ll1$ and can be identified with symmetric GIT quotients of $(\mathbb{P}^1)^n$ by the diagonal action of $\mathbb{G}_m$ when $n$ is odd, and their Kirwan desingularization when $n$ is even. The existence of such an exceptional collection is one of the needed ingredients in order to prove the existence of a full $S_n$-invariant exceptional collection on $\overline{\mathcal{M}}_{0,n}$. To prove exceptionality we use the method of windows in derived categories. To prove fullness we use previous work on the existence of invariant full exceptional collections on Losev-Manin spaces. |
| title | Exceptional collections on certain Hassett spaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2005.00751 |