UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

February 22, 2011

939 Evans Hall

3:45PM: Castelnuovo-Mumford regularity of seminormal simplicial affine semigroup rings

Max Nitsche

The Eisenbud-Goto conjecture has been open for over 25 years, even for affine semigroup rings the conjecture is widely open. In this talk we will focus on simplicial affine semigroup rings, moreover we will discuss the latest results in the seminormal case.

5:00PM: Secant varieties of toric varieties

Claudiu Raicu

Following a paper by Cox and Sidman, I will describe a method for computing the degree of the variety of secant lines to a smooth projective toric variety, embedded via a complete linear system. In low dimension, this method yields explicit formulas in terms of the combinatorics of the associated lattice polytope. It also gives the degree of the secant variety of an arbitrary Segre-Veronese variety.

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