The Moduli of Flat U(p, 1) Structures on Riemann Surfaces

被引：0

作者：

Eugene Z. Xia

机构：

[1] National Cheng-Kung University,Department of Mathematics

来源：

Geometriae Dedicata | 2003年 / 97卷

关键词：

algebraic curves; Higgs bundles; moduli schemes;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

For X a smooth projective curve over ℂ of genus g > 1, Hom+(π1(X), U(p, 1))/U(p, 1) is the moduli space of flat semi-simple U(p, 1)-connections on X. There is an integer invariant, τ, the Toledo invariant associated with each element in Hom+(π1(X), U(p, 1))/U(p, 1). This paper shows that Hom+(π1(X), U(p, 1))/U(p, 1) has one connected component corresponding to each τ & in 2 ℤ with −2(g−1) ≤τ≤2(g−1). Therefore the total number of connected components is 2(g−1)+1.

引用

页码：33 / 43

页数：10

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