Hodge Bundles on Smooth Compactifications of Siegel Varieties and Applications
Abstract
We study Hodge bundles on Siegel varieties and their various extensions to smooth toroidal compactifications. Precisely, we construct a canonical Hodge bundle on an arbitrary Siegel variety so that the holomorphic tangent bundle can be embedded into the Hodge bundle, and we observe that the Bergman metric on the Siegel variety is compatible with the induced Hodge metric. Therefore we obtain the asymptotic estimate of the Bergman metric explicitly. Depending on these properties and the uniformitarian of K\"ahler-Einstein manifold, we study extensions of the tangent bundle over any smooth toroidal compactification. We also apply this result, together with Siegel cusp modular forms, to study general type for Siegel varieties.
Keywords
Cite
@article{arxiv.1201.3784,
title = {Hodge Bundles on Smooth Compactifications of Siegel Varieties and Applications},
author = {Shing-Tung Yau and Yi Zhang},
journal= {arXiv preprint arXiv:1201.3784},
year = {2014}
}
Comments
typos correction and some improvements 28pages