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Semi-canonical embeddings for rational compexity-one T-varieties

Banff International Research Station for Mathematical Innovation and Discovery

A normal affine toric variety X with no torus factors has a canonical equivariant embedding in affine space, determined by the Hilbert basis of the weight cone of X. This embedding has many nice properties: the tropicalization Trop(X) with respect to this embedding is a linear subspace of R^n, every initial ideal corresponding to a point in Trop(X) is simply the ideal of X, and the generators for the coordinate ring of X form a Khovanskii basis with respect to any full-rank homogeneous valuation. In this talk, I will report on joint work with Nathan Ilten in which we generalize this situation to normal rational affine varieties equipped with the action of a codimension-one torus. We produce explicit affine embeddings of such varieties, and show that these embeddings enjoy properties similar to those found in the toric situation.

Mathematics; Algebraic geometry; Convex and discrete geometry

video/mp4

Author affiliation: George Mason University

2017-11-06

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/63543

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/