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AG2: Algebraic Geometry
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Euler characteristics of subvarieties of tropical abelian varieties 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. Tropical reductive groups and principal bundles on metric graphs 1: Goethe University Frankfurt, Germany; 2: Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany; 3: Paderborn University, Germany; 4: Central Michigan University, USA In this talk I will explain of our proposed elementary tropical analogue of a reductive group that combines the datum of a Weyl group and the tropicalization of a fixed maximal torus. For the classical groups these tropical reductive groups admit descriptions as tropical matrix groups that resemble their classical counterparts. Employing this perspective, one can introduce tropical principal bundles on metric graphs and study their explicit presentations as pushforwards of line bundles along covers with symmetries and extra data. The main result identifies the essential skeleton of the moduli space of semistable principal bundles on a Tate curve with its tropical analogue. | ||
