Bruno De Oliveira : CMS criterion and the geography of surfaces with big cotangent bundle
Posted by Izzet Coskun , part of the Algebraic Geometry Seminar.
- At
- April 15, 2024, 3 p.m.
- In
- 636 SEO
- Abstract
- We investigate the components determining bigness of the cotangent bundle $\Omega^1_X$ of smooth models $X$ in the birational class $\mathcal {Y}$ of an orbifold surface of general type $Y$, with a focus on the contribution given by the singularities of $Y$. A criterion for bigness of $\Omega_X^1$ is given involving only topological and singularity data on $Y$. We single out a special case, the Canonical Model Singularities (CMS) criterion, when $Y$ is the canonical model of $\mathcal Y$. We study the singularity invariants appearing in the criterion and determine them for $A_n$ singularities. Knowledge of these invariants for $A_n$ singularities allows one to evaluate the $(c_2,c^2_1)-$geographical range of the CMS criterion and compare it to other criteria. We obtain new examples of surfaces with big cotangent bundle. (Joint work with Y. Asega and M.Weiss)