UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

April 03, 2018

939 Evans Hall

3:45PM: Curves on a smooth cubic surface in P3

Mengyuan Zhang

We examine effective divisors on a smooth cubic surface in P3. By means of Zariski decomposition, we reveal the interplay between the geometry of secant lines and cohomologies of line bundles. We also describe the degrees of the generators of the Hartshorne-Rao modules. Finally we determine the free resolutions of the curves. The work is a simplification, correction and generalization of the work of Giuffrida and Maggioni.

5:00PM: An introduction to Liaison

Christopher Eur

We give a gentle introduction to liaison of algebraic varieties following Peskine-Szpiro. We will carefully go through the basic definitions and properties, along with various examples, in preparation for subsequent talks on the linkage of space curves.

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