## Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring: Curves on a smooth cubic surface in P3

Seminar | April 3 | 3:45-5 p.m. | 939 Evans Hall

Mengyuan Zhang, UC Berkeley

Department of Mathematics

We examine effective divisors on a smooth cubic surface in $\mathbf {P^3}$. 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.

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