## Commutative Algebra Seminar

Takumi Murayama

University of Michigan

Combining asymptotic invariants of singularities and of line bundles

**Abstract:**A common trend in algebraic geometry and commutative algebra is to associate asymptotic invariants to various objects, such as line bundles or families of ideals. In particular, Seshadri constants measure how close a line bundle is to being very ample, and can be defined by combining the volume function from geometry with the Hilbert-Samuel multiplicity function from algebra, thereby combining both geometric and local algebraic information into one invariant. We will describe how this point of view together with Frobenius techniques in commutative algebra can be used instead of vanishing theorems to prove effective positivity results over the complex numbers in the direction of Fujita's conjecture.

Monday October 1, 2018 at 3:00 PM in 612 SEO