Algebraic Geometry Seminar

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CMS criterion and the geography of surfaces with big cotangent bundle

Speaker: Bruno de Oliveira, University of Miami

Location: Warren Weaver Hall 512

Date: Tuesday, February 27, 2024, 3:30 p.m.

Synopsis:

(Joint work with Y. Asega and M.Weiss)

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.