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/pdf/divisor-classes-associated-to-families-of-stable-varieties-ilcszsgsda.pdf

Divisor classes associated to families of stable varieties, with applications to the moduli space of curves

The background of this paper is the following conjecture on complex surfaces of general type: Let S be a (smooth, projective) minimal surface of general type over ti? with c~ 2 throughout the paper.

Fibered Algebraic Surfaces with Low Slope

The aim of this paper is to study the modified diagonal cycle in the triple product of a curve over a global field defined by Gross and Schoen. Our main result is an identity between the height of this cycle and the self-intersection of the relative dualising sheaf. We have some applications to the following problems in number theory and algebraic geometry.

Gross-Schoen cycles and dualising sheaves

Let f : X → Y be a semistable family of complex abelian varieties over a curve Y of genus g(Y ), and smooth over the com

/pdf/a-characterization-of-certain-shimura-curves-in-the-moduli-1a9zufx3ko.pdf

A characterization of certain shimura curves in the moduli stack of abelian varieties

In this note, we rst establish a connection between the weight in the geo- metric invariant theory and the height introduced by Cornalba and Harris (CH) and Zhang (Z). Then we give two applications. First, it provides a converse of Cornalba and Harris's result, which can be treated as a function eld analogue of Zhang's theorem over number eld. In particular, this connection gives a numerical interpretation of the moral stability = positivity that was advocated by Viehweg. Second, we relate these to the study the positivity of CM-line bundle introduced by Tian and the determinant line bundle introduced by Donaldson.

/pdf/height-and-git-weight-nc455tdvwn.pdf

Xiao Gang

Papers

Fibered Algebraic Surfaces with Low Slope

Algebraic surfaces with high canonical degree