Algebraic Geometry Seminar
Bruno De Oliveira
University of Miami
CMS criterion and the geography of surfaces with big cotangent bundle
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)
Monday April 15, 2024 at 3:00 PM in 636 SEO