Vincent Koziarz

TL;DR: In this paper, the authors define an invariant associe aux representations dans PU(n, 1) des groupes fondamentaux des surfaces orientables de type topologique fini and de caracteristique d'Euler negative.

TL;DR: In this paper, it was shown that given a lc pair $(X, \Delta), a large enough multiple of the bundle $K_X+ \Delta$ is effective provided that its Chern class contains an effective $\bQ$-divisor.

TL;DR: In this article, Burger and Iozzi showed that if a representation is reductive and if m is at least 2, then there exists a finite energy harmonic equivariant map from complex hyperbolic m-space to complex polygonal n-space.

Abstract: Let Г be a torsion-free uniform lattice of SU(m, 1), m > 1. Let G be either SU(p, 2) with p ≥ 2, \({{\rm Sp}(2,\mathbb {R})}\) or SO(p, 2) with p ≥ 3. The symmetric spaces associated to these G’s are the classical bounded symmetric domains of rank 2, with the exceptions of SO*(8)/U(4) and SO*(10)/U(5). Using the correspondence between representations of fundamental groups of Kahler manifolds and Higgs bundles we study representations of the lattice Г into G. We prove that the Toledo invariant associated to such a representation satisfies a Milnor-Wood type inequality and that in case of equality necessarily G = SU(p, 2) with p ≥ 2m and the representation is reductive, faithful, discrete, and stabilizes a copy of complex hyperbolic space (of maximal possible induced holomorphic sectional curvature) holomorphically and totally geodesically embedded in the Hermitian symmetric space SU(p, 2)/S(U(p) × U(2)), on which it acts cocompactly.

TL;DR: In this article, the authors studied various concrete algebraic and differential geometric properties of the Cartwright-Steger surface and determined the genus of a generic fiber of the Albanese fibration.