Nasjonalt algebramøte 2018: Jarle Stavnes
Jarle Stavnes, UiO: Toric degenerations modeled on polyhedral manifolds
Abstract: The Gross-Siebert program for mirror symmetry seeks to use toric degenerations associated to polyhedral manifolds to generalize the Batyrev-Borisov construction of 1-parameter families of Calabi Yau hypersurfaces in toric Fano varieties, along with their mirrors. The special fiber of a toric degeneration is a projective variety stratified by tori, and the polyhedral manifold is a combinatorial counterpart analogous to the correspondence between toric varieties and polytopes. I will give an account of this correspondence, and explain how some deformation theoretic results on Stanley-Reisner schemes can be extended to such stratifications by tori in the 2-dimensional case.