Tim Gräfnitz (Hamburg)
8 April 2021
"Tropical correspondence for smooth del Pezzo log Calabi-Yau pairs"
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 \ge 3 and a smooth anticanonical divisor D. The easiest example of such a pair is (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.
8 April 2021
"Tropical correspondence for smooth del Pezzo log Calabi-Yau pairs"
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 \ge 3 and a smooth anticanonical divisor D. The easiest example of such a pair is (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.
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