Back to Algebraic Geometry Seminar: Fall 2016
Algebraic Geometry Seminar
Date: Tuesday, Sep 20, 2016
Time: 3:30PM - 4:30PM
Location: LCB 222
Lei Song
University of Kansas
Title |
On normal generation of line bundles on a surface |
Abstract |
Let $L$ be a line bundle on a smooth projective surface $X$. A conjecture attributed to S. Mukai says if $L\simeq \omega_{X}\otimes A^{\otimes k}$ for some ample line bundle $A$ and an integer $k\ge 4$, then $L$ is normally generated. In this talk, I will discuss various methods and results in the curve and surface case. I will show the conjecture holds for a double covering over an anticanonical rational surface, which may be viewed as a two dimensional analogue of hyper-elliptic curve, and equivariant ample line bundle $A$. The work builds on an understanding of linear systems on anticanonical rational surfaces, which is largely due to B. Harbourne. |
Algebraic Geometry