Back to Commutative Algebra Seminar: Fall 2019
Commutative Algebra Seminar
Date: Friday, Sep 6, 2019
Time: 2:30PM - 3:20PM
Location: LCB 225
Bangere Purnaprajna
University of Kansas, Lawrence
Title |
Deformation of canonical morphisms and moduli spaces |
Abstract |
In this talk we will deal with the deformation of finite maps and show how to use this deformation theory to construct varieties with given invariants in a projective space. Among other things, we show a criterion that determines when a finite map can be deformed to a one–to–one map. We use this general result that holds for all dimensions, to construct new surfaces of general type with birational canonical map, for different $c_1^2$ and $\chi$ (the canonical map of the surfaces we construct is in fact a finite, birational morphism), addressing a question of Enriques posed in 1944. All known families until now were complete intersections or divisors in three folds. Our results enable us to describe some new components of the moduli of surfaces of general type. We find infinitely many moduli spaces $\mathcal M_{(x’,0,y)}$ having one component whose general point corresponds to a canonically embedded surface and another component whose general point corresponds to a surface whose canonical map is a degree $2$ morphism, the so called hyperelliptic components. In recent weeks we have proved analogues of these results for varieties of general type in all dimensions.This is part of joint work with F. J. Gallego and M. Gonzalez. |
Commutative Algebra