arXiv subjects

Silke Lekaus

Publications and source records attributed to Silke Lekaus.

2 recordsLinked to original sources

arXiv2003

Unipotent flat bundles and Higgs bundles over compact Kaehler manifolds

We characterize those unipotent representations of the fundamental group $π_1(X,x)$ of a compact Kaehler manifold $X$, which correspond to a Higgs bundle whose underlying Higgs field is equal to zero. The characterization is parallel to the one that R. Hain gave of those unipotent representations of $π_1(X,x)$ that can be realized as the monodromy of a flat connection on the holomorphically trivial vector bundle. We see that Hain's result and ours follow from a careful study of Simpson's correspondence between Higgs bundles and local systems.

math.AG↗

arXiv2000

Relation between the dimensions of the ring generated by a vector bundle of degree zero on an elliptic curve and a torsor trivializing this bundle

M. Nori proved that on a projective smooth variety, a bundle is finite, (that is the ring it generates has dimension 0), if and only if it trivializes on a finite cover. In this note, we consider bundles of degree 0 on an elliptic curve. We prove that the dimension of the ring generated by such a bundle is the same as the dimension of a torsor trivializing the bundle (and is 1).

math.AG↗