arXiv subjects

Pascal Dingoyan

Publications and source records attributed to Pascal Dingoyan.

3 recordsLinked to original sources

arXiv2018

Application of Cheeger-Gromov theory to the $l^2$-cohomology of harmonic Higgs bundles over covering of finite volume complete manifolds

We review and apply Cheeger-Gromov theory on $l^2$-cohomology of infinite coverings of complete manifolds with bounded curvature and finite volume. Applications focus on $l^2$-cohomology of (pullback of) harmonic Higgs bundles on some covering of Zariski open sets of K\"ahler manifolds. The $l^2-$Dolbeault to DeRham spectral sequence of these Higgs bundles is seen to degenerate at $E_2$.

math.CV↗

arXiv2014

A factorisation theorem for curve with vanishing self-intersection

Let C be a curve in a compact Kahler surface Y. Assume that the self-intersection of C is vanishing, and the image of the fundamental group of C in Y is of infinite index in the fundamental group of Y. Does it follow that C is a fiber of a holomorphic map from Y to a curve ? We give, in some cases, a positive answer to the question. Our strategy is to solve a Poincare-Lelong equation on some infinite covering of Y.

math.CV↗

arXiv2010

Some mixed Hodge structure on l^2-cohomology of covering of K\"ahler manifolds

We give methods to compute l^2-cohomology groups of a covering manifolds obtained by removing pullback of a (normal crossing) divisor to a covering of a compact K\"ahler manifold. We prove that in suitable quotient categories, these groups admit natural mixed Hodge structure whose graded pieces are given by expected Gysin maps.

math.CV↗