Back to Algebraic Geometry Seminar: Spring 2016
Algebraic Geometry Seminar
Date: Tuesday, Jan 26, 2016
Time: 3:30PM - 4:30PM
Location: JFB 102
2:50 - 3:50PM JFB 102
Nicolas Addington
University of Oregon
Title |
Lehn's hyperkahler 8-fold associated to a cubic 4-fold |
Abstract |
Compact hyperkahler varieties are higher-dimensional analogues of K3 surfaces. Very few examples are known: two infinite series and two sporadic examples. At the same time we cannot prove that there are not many more examples. In 2013, Lehn et al. constructed a family of hyperkahler 8-folds Z from the variety of twisted cubic curves on a cubic 4-fold. I will discuss some joint work with Lehn from 2014 and some new work, which together clarify Z’s place in the moduli space of hyperkahlers. In particular it is deformation-equivalent, but typically not isomorphic or even birational, to the Hilbert scheme of 4 points on a K3 surface. A crucial role is played by Kuznetsov’s K3 subcategory of the derived category of the cubic. |
Algebraic Geometry