The contraction morphism between maps and quasimaps to toric varieties
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917875989610496 |
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| author | Rabano, Alberto Cobos |
| author_facet | Rabano, Alberto Cobos |
| contents | Given $X$ a smooth projective toric variety, we construct a morphism from a closed substack of the moduli space of stable maps to $X$ to the moduli space of quasimaps to $X$. If $X$ is Fano, we show that this morphism is surjective. The construction relies on the notion of degree of a quasimap at a base-point, which we define. We show that a quasimap is determined by its regular extension and the degree of each of its basepoints. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_16295 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The contraction morphism between maps and quasimaps to toric varieties Rabano, Alberto Cobos Algebraic Geometry 14D20 (Primary) 14M25, 14N35 (Secondary) Given $X$ a smooth projective toric variety, we construct a morphism from a closed substack of the moduli space of stable maps to $X$ to the moduli space of quasimaps to $X$. If $X$ is Fano, we show that this morphism is surjective. The construction relies on the notion of degree of a quasimap at a base-point, which we define. We show that a quasimap is determined by its regular extension and the degree of each of its basepoints. |
| title | The contraction morphism between maps and quasimaps to toric varieties |
| topic | Algebraic Geometry 14D20 (Primary) 14M25, 14N35 (Secondary) |
| url | https://arxiv.org/abs/2412.16295 |