Tropical correspondence for smooth del Pezzo log Calabi-Yau pairs

Abstract: In this talk I will present the main results of my thesis, a tropical correspondence theorem for log Calabi-Yau pairs $(X,D)$ consisting of a smooth del Pezzo surface $X$ of degree $\ge3$ and a smooth anticanonical divisor $D$. The easiest example of such a pair is $(\mathbb{P}^2,E)$, where $E$ is an elliptic curve. I will explain how the genus zero logarithmic Gromov-Witten invariants of $X$ with maximal tangency to $D$ are related to tropical curves in the dual intersection complex of $(X,D)$ and how they can be read off from the consistent wall structure appearing in the Gross-Siebert program. The novelty in this correspondence is that $D$ is smooth but non-toric, leading to log singularities in the toric degeneration that have to be resolved.

algebraic geometrycombinatorics

Audience: researchers in the topic

( slides | video )

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Online Nottingham algebraic geometry seminar

Series comments: Online geometry seminar, typically held on Thursday. This seminar takes place online via Microsoft Teams on the Nottingham University "Algebraic Geometry" team.

For recordings of past talks, copies of the speaker's slides, or to be added to the Team, please visit the seminar homepage at: kasprzyk.work/seminars/ag.html

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