Chern ratios of surfaces with big cotangent bundle

Date/heure
9 décembre 2024
14:00 - 15:00

Lieu
Salle de conférences Nancy

Oratrice ou orateur
Bruno De Oliveira

Catégorie d'évènement
Séminaire de géométrie complexe

We introduce the canonical model singularities (CMS) criterion for bigness of the cotangent bundle for surfaces. The CMS-criterion for bigness involves invariants for canonical singularities that we describe and we give formulas for A_n singularities. The CMS-criterion leads to conjectures and some answers about the geography and the possible ratios $c_1^2/c_2$ of surfaces with big cotangent bundle. Two cases are naturally separated: regular and irregular surfaces. For regular surfaces we apply the CMS-criterion to show the existence of deformations of hypersurfaces in ${\mathbb{P}}^3$ with big cotangent bundle for degree $d\ge 8$ and give an example of the regular surface with big  cotangent bundle with ratio close to 1/5. For irregular surfaces we show that there are examples with ratio as close to 1/5 as possible. If time permits, we talk about ratios  below 1/5.