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Session

AG2: Algebraic Geometry Location: A701 Session Chair: Mateusz Michalek Session Chair: Botong Wang

Presentation 1

Euler characteristics of subvarieties of tropical abelian varieties Scott Hiatt1, Connor Simpson2, Botong Wang1, Chenxi Wu1 1: University of Wisconsin-Madison; 2: University of Sydney and SMRI Let $X$ be a smooth subvariety of a complex abelian variety. A theorem of Green and Lazarsfeld states that the Euler characteristic of $\mathcal{O}_X$ has sign $(-1)^{\dim X}$. In this talk, we discuss a tropical analogue of this result. Under suitable assumptions, we prove that the topological Euler characteristic of a subvariety of a tropical abelian variety is also determined by its dimension, following the same sign formula. This is joint work with Scott Hiatt, Connor Simpson, and Chenxi Wu.