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Counting (tropical) curves via scattering.sage

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arxiv 2210.10455 v1 pith:WZV7KAU7 submitted 2022-10-19 math.AG

classification math.AG
keywords scatteringwillcomputingdiagramsexplainsagetropicalalgebro-combinatorial
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abstract

In this note I will explain how relative/log Gromov-Witten invariants of pairs $(X,D)$ with very ample smooth anticanonical divisor $D$ can be computed using algebro-combinatorial objects called scattering diagrams. The underlying principle behind this computational method is a tropical correspondence theorem for non-toric cases, which I will explain briefly. By computing some examples I will give an introduction to a sage code that I wrote for computing scattering diagrams.

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  1. Sesquicuspidal curves, scattering diagrams, and symplectic nonsqueezing

    math.AG 2024-11 conditional novelty 8.0 of 10

    The stabilized symplectic embedding capacity of the round four-ball is computed exactly: a Fibonacci staircase below tau^4, then 3a/(a+1).

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