Fundamental Groups in Arithmetic and Algebraic Geometry

# Symmetric differentials and the fundamental group

speaker: Bruno Klingler (Université Paris-Diderot - Institut Mathématique de Jussieu )

abstract: Esnault asked whether every smooth complex projective variety with infinite fundamental group has a nonzero symmetric differential (a section of a symmetric power of the cotangent bundle). In a sense, this would mean that every variety with infinite fundamental group has some nonpositive curvature. We show that the answer to Esnault's question is positive when the fundamental group has a finite-dimensional representation over some field with infinite image. This applies to all known varieties with infinite fundamental group. Along the way, we produce many symmetric differentials on the base of a variation of Hodge structures.

timetable:
Mon 16 Dec, 15:00 - 16:00, Aula Dini
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