Projections in toric degenerations and standard monomials

Abstract: I will report on joint work in progress with Takuya Murata. We study toric degenerations, i.e. flat morphism of a normal variety to the affine line whose generic fibre is isomorphic to a fixed projective variety and whose special fibre is a projective toric variety. Although such a flat morphism may be given abstractly (i.e. without an embedding, for example a toric scheme over the affine line) using valuations and Gröbner theory we may restrict our attention to the case where our family comes endowed with an embedding. I will illustrate an example of an elliptic curve where a toric degeneration admits a projection from the generic fibre (the elliptic curve) to the special fibre (the toric curve). We want to understand which kind of (embedded) toric degenerations admit such a projection. The notion of standard monomials in Gröbner theory proves to be a useful tool in constructing projections in arbitrary toric degenerations.

algebraic geometrynumber theory

Audience: researchers in the topic

SFU NT-AG seminar

Series comments: Description: Research/departmental seminar

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