Exposition: Enumerative Geometry and Tree-Level Gromov-Witten Invariants
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909449502851072 |
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| author | Anderson, Reginald |
| author_facet | Anderson, Reginald |
| contents | Here we review background in differential topology related to the calculation of an euler characteristic, and background on localization in equivariant cohomology. We then outline Gromov-Witten invariants in algebraic geometry and give examples of the genus 0 Gromov-Witten potential for $\PP^1, \PP^2$, and a genus $g>0$ Riemann surface. Kontsevich-Manin's recursive formula for $N_d$, the number of degree $d$ rational curves through $3d-1$ points in general position on $\PP^2$ is recovered. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03232 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exposition: Enumerative Geometry and Tree-Level Gromov-Witten Invariants Anderson, Reginald General Mathematics 14-02, 14N35 Here we review background in differential topology related to the calculation of an euler characteristic, and background on localization in equivariant cohomology. We then outline Gromov-Witten invariants in algebraic geometry and give examples of the genus 0 Gromov-Witten potential for $\PP^1, \PP^2$, and a genus $g>0$ Riemann surface. Kontsevich-Manin's recursive formula for $N_d$, the number of degree $d$ rational curves through $3d-1$ points in general position on $\PP^2$ is recovered. |
| title | Exposition: Enumerative Geometry and Tree-Level Gromov-Witten Invariants |
| topic | General Mathematics 14-02, 14N35 |
| url | https://arxiv.org/abs/2501.03232 |