Tropical super Gromov-Witten invariants
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914104112840704 |
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| author | Sheshmani, Artan Yau, Shing-Tung Zhou, Benjamin |
| author_facet | Sheshmani, Artan Yau, Shing-Tung Zhou, Benjamin |
| contents | We show that super Gromov-Witten invariants can be defined and computed by methods of tropical geometry. When the target is a point, the super invariants are descendant invariants on the moduli space of curves, which can be computed tropically. When the target is a convex, toric variety $X$, we describe a procedure to compute the tropical Euler class of the SUSY normal bundle $\overline{N}_{n, β}$ on $\overline{\mathcal{M}}_{0,n}(X, β)$, assuming it is locally tropicalizable in the sense of [CG], [CGM]. Then, we define the tropical, genus-0, $n$-marked, super Gromov-Witten invariant of $X$, and compute an example. This gives a tropical interpretation of super Gromov-Witten invariants of convex, toric varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_17400 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tropical super Gromov-Witten invariants Sheshmani, Artan Yau, Shing-Tung Zhou, Benjamin Algebraic Geometry Mathematical Physics Combinatorics We show that super Gromov-Witten invariants can be defined and computed by methods of tropical geometry. When the target is a point, the super invariants are descendant invariants on the moduli space of curves, which can be computed tropically. When the target is a convex, toric variety $X$, we describe a procedure to compute the tropical Euler class of the SUSY normal bundle $\overline{N}_{n, β}$ on $\overline{\mathcal{M}}_{0,n}(X, β)$, assuming it is locally tropicalizable in the sense of [CG], [CGM]. Then, we define the tropical, genus-0, $n$-marked, super Gromov-Witten invariant of $X$, and compute an example. This gives a tropical interpretation of super Gromov-Witten invariants of convex, toric varieties. |
| title | Tropical super Gromov-Witten invariants |
| topic | Algebraic Geometry Mathematical Physics Combinatorics |
| url | https://arxiv.org/abs/2510.17400 |