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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2308.06844 |
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| _version_ | 1866929246239195136 |
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| author | Chekeres, Olga Kandel, Santosh Losev, Andrey Mnev, Pavel Wernli, Konstantin Youmans, Donald R. |
| author_facet | Chekeres, Olga Kandel, Santosh Losev, Andrey Mnev, Pavel Wernli, Konstantin Youmans, Donald R. |
| contents | We address the question of counting maps between projective spaces such that images of cycles on the source intersect cycles on the target. In this paper we do it by embedding maps into quasimaps that form a projective space of their own. When a quasimap is not a map, it contains freckles (studied earlier) and/or scars, appearing when the complex dimension of the source is greater than one. We consider a lot of examples showing that freckle/scar calculus (using excess intersection theory) works. We also propose the "smooth conjecture" that may lead to computation of the number of maps by an integral over the space of quasimaps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_06844 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On enumerative problems for maps and quasimaps: freckles and scars Chekeres, Olga Kandel, Santosh Losev, Andrey Mnev, Pavel Wernli, Konstantin Youmans, Donald R. Mathematical Physics We address the question of counting maps between projective spaces such that images of cycles on the source intersect cycles on the target. In this paper we do it by embedding maps into quasimaps that form a projective space of their own. When a quasimap is not a map, it contains freckles (studied earlier) and/or scars, appearing when the complex dimension of the source is greater than one. We consider a lot of examples showing that freckle/scar calculus (using excess intersection theory) works. We also propose the "smooth conjecture" that may lead to computation of the number of maps by an integral over the space of quasimaps. |
| title | On enumerative problems for maps and quasimaps: freckles and scars |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2308.06844 |