Algebraic Geometry Seminar

---

Extremal cotangent dimension for surfaces of general type

Speaker: Bruno De Oliveira, University of Miami

Location: Warren Weaver Hall 512

Date: Tuesday, April 21, 2026, 5 p.m.

Synopsis:

Until 2026, there were no examples of minimal surfaces of general type with nontrivial symmetric differentials if the slope c_1^2/c_2<1/5. All known tools to produce symmetric differentials naturally failed in the region c_1^2/c_2<1/5.  We examine the forbidden region via two new tools. Concerning maximal cotangent dimension, i.e. the cotangent bundle is big,  we focus on new results and examples coming examining the possible presence of a fibration whose orbifold base is of Campana general type. Concerning minimal cotangent dimension, i.e. absence of symmetric differentials, the approach uses double covers and symmetric logarithmic differentials on the base. We give special attention to the class of surfaces named Horikawa surfaces. This talk describes joint work with D. Brotbek and E. Rousseau.