On surfaces of general type with extremal cotangent dimension

Abstract: In this talk we give a brief survey on the cotangent dimension for surfaces. Then we present several results describing general conditions that guarantee that a surface has maximal cotangent dimension, i.e. it is big. We focus on an approach via fibrations whose orbifold base is of Campana general type. Finally, we address minimal cotangent dimension, i.e. absence of symmetric differentials, for surfaces of general type. Here, the approach uses double covers and symmetric logarithmic differentials. We give special attention to the class of surfaces named Horikawa surfaces. This talk describes joint work with D. Brotbek and E. Rousseau.

mathematical physicsalgebraic geometryalgebraic topologydifferential geometryrepresentation theorysymplectic geometry

Audience: researchers in the topic

Geometry and Physics @ Lisbon