Homology of spaces of curves on blowups
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911007906988032 |
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| author | Das, Ronno Tosteson, Philip |
| author_facet | Das, Ronno Tosteson, Philip |
| contents | We consider the space of holomorphic maps from a compact Riemann surface to a projective space blown up at finitely many points. We show that the homology of this mapping space equals that of the space of continuous maps that intersect the exceptional divisors positively, once the degree of the maps is sufficiently positive compared to the degree of homology. The proof uses a version of Vassiliev's method of simplicial resolution. As a consequence, we obtain a homological stability result for rational curves on the degree $5$ del Pezzo surface, which is analogous to a case of the Batyrev--Manin conjectures on rational point counts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_12968 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Homology of spaces of curves on blowups Das, Ronno Tosteson, Philip Algebraic Topology Algebraic Geometry 58D15, 55R80, 14H50, 14H99 We consider the space of holomorphic maps from a compact Riemann surface to a projective space blown up at finitely many points. We show that the homology of this mapping space equals that of the space of continuous maps that intersect the exceptional divisors positively, once the degree of the maps is sufficiently positive compared to the degree of homology. The proof uses a version of Vassiliev's method of simplicial resolution. As a consequence, we obtain a homological stability result for rational curves on the degree $5$ del Pezzo surface, which is analogous to a case of the Batyrev--Manin conjectures on rational point counts. |
| title | Homology of spaces of curves on blowups |
| topic | Algebraic Topology Algebraic Geometry 58D15, 55R80, 14H50, 14H99 |
| url | https://arxiv.org/abs/2405.12968 |