|Speaker:||Makoto Miura (University of Tokyo)|
|Title:||Toric degenerations of Grassmann manifolds and mirror symmetry|
|Date (JST):||Mon, Aug 30, 2010, 14:00 - 17:00|
|Place:||Seminar Room A|
I will talk about the theory of toric degenerations and its application to a construction of conjectural mirror families for complete intersection Calabi-Yau manifolds in Grassmann manifolds. I will
introduce the theory of sagbi basis, a subalgebra version of Grobner basis for ideals, and discuss the relations to Sturmfels' flat toric degenerations.
I will talk about the toric degenerations in more detail, aiming to extend the mirror constructions for complete intersection Calabi-Yau 3-folds in ordinary Grassmannians to other types. It turns out that, for suitable degenerations, we have to choose a term order for which the homogeneous coordinate ring has an uniformly homogeneous sagbi basis. We classify these term orders for some special cases of ordinary Grassmannians and orthogonal Grassmannians.