# Periods of tropical K3 hypersurfaces

• Yuto Yamamoto (University of Tokyo)
• Friday 11 May 2018, 15:00-16:00
• MR13.

Let $\Delta$ be a smooth reflexive polytope in dimension 3 and $W$ be a tropical polynomial whose Newton polytope is the polar dual of $\Delta$. One can construct a $2$-sphere equipped with an integral affine structure with singularities by contracting the tropical K3 hypersurface defined by $W$. We write the complement of the singularity as $i \colon B_0 \hookrightarrow B$, and the local system of integral tangent vectors on $B_0$ as $T$. In the talk, we will give a primitive embedding of the Picard group $\mathrm{Pic} X$ of the toric variety $X$ associated with the normal fan of $\Delta$ into $H^1(B, i_\ast T)$, and compute the radiance obstruction of $B$, which sits in the image of $\mathrm{Pic} X$.

This talk is part of the Junior Geometry Seminar series.