# Periods of tropical K3 hypersurfaces

2019/05/17 Fri 10:30 - 12:00

3号館152号室

Let $\Delta$ be a smooth reflexive polytope in dimension 3 and $f$ be a tropical polynomial whose Newton polytope is the polar dual of $\Delta$. One can construct a $2$-sphere $B$ equipped with an integral affine structure with singularities by contracting the tropical K3 hypersurface defined by $f$. We write the complement of the singularity as $\iota \colon B_0 \hookrightarrow B$, and the local system of integral tangent vectors on $B_0$ as $\mathcal{T}_\mathbb{Z}$. Let further $Y$ be an anti-canonical hypersurface of the toric variety associated with the normal fan of $\Delta$, and $\mathrm{Pic} (Y)_\mathrm{amb}$ be the sublattice of $\mathrm{Pic}(Y)$ coming from the ambient space. We give a primitive lattice embedding $\mathrm{ Pic} (Y)_\mathrm{amb} \hookrightarrow H^1(B, \iota_\ast \mathcal{T}_\mathbb{Z})$, and compute the radiance obstruction of $B$, which sits in the subspace generated by the image of $\mathrm{Pic} (Y)_\mathrm{amb}$.