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Apr 15 2024

Algebraic Geometry Seminar: CMS criterion and the geography of surfaces with big cotangent bundle, by Bruno De Oliveira

April 15, 2024

3:00 PM - 3:50 PM


636 SEO


Chicago, IL

Bruno De Oliveira (University of Miami): CMS criterion and the geography of surfaces with big cotangent bundle

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)

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Izzet Coskun

Date posted

Mar 3, 2024

Date updated

Mar 3, 2024