Hodge Bundles on Smooth Compactifications of Siegel Varieties and Applications

Shing-Tung Yau Harvard University Yi Zhang Fudan University

Algebraic Geometry Arithmetic Geometry and Commutative Algebra mathscidoc:1706.01001

Siegel varieties are locally symmetric varieties. They are important and interesting in algebraic geometry and number theory. We construct a canonical Hodge bundle on a Siegel variety so that the holomorphic tangent bundle can be embedded into the Hodge bundle; we obtain that the canonical Bergman metric on a Siegel variety is same as the induced Hodge metric and we describe asymptotic behavior of this unique K\"ahler-Einstein 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 apply these results of Hodge bundles, to study dimension of Siegel cusp modular forms and general type for Siegel varieties
Hogde bundles, Siegel variety, Siegel modular form, compactifications
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  title={Hodge Bundles on Smooth Compactifications of Siegel Varieties and Applications},
  author={Shing-Tung Yau, and Yi Zhang},
Shing-Tung Yau, and Yi Zhang. Hodge Bundles on Smooth Compactifications of Siegel Varieties and Applications. 2017. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170603143928224749788.
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