HODGE POLYNOMIALS OF THE MODULI SPACES OF TRIPLES OF RANK (2, 2)
HODGE POLYNOMIALS OF THE MODULI SPACES OF TRIPLES OF RANK (2, 2)
复制标题
三元组模空间的霍奇多项式 (2, 2)
DOI：
10.1093/qmath/han007
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发表时间：
2007
影响因子：
0.7
通讯作者：
M. J. V'azquez
中科院分区：
文献类型：
--
作者：
V. Muñoz;Daniel Ortega;M. J. V'azquez
设X是亏格g≥2在复数上的光滑射影曲线。X上的全纯三元组(E1，E2，φ)由X上的两个全纯向量丛E1和E2组成
和全纯映射φ：E_2，→_1。有一个三元组稳定性的概念，它依赖于一个实参数σ。本文利用混合Hodge结构理论，确定了Rk(E_1)=Rk(E_2)=2的σ-稳定三元组的模空间的Hodge多项式
它们是光滑和紧凑的)。这特别给出了这些模空间的Poincar‘e多项式。作为副产品，我们还给出了偶数次秩2稳定向量丛的模空间的Hodge多项式。
Let X be a smooth projective curve of genus g ≥ 2 over the complex numbers. A holomorphic triple (E1, E2, φ) on X consists of two holomorphic vector bundles E1 and E2 over X
and a holomorphic map φ: E2 → E1. There is a concept of stability for triples which depends on a real parameter σ. In this paper, we determine the Hodge polynomials of the moduli spaces of σ-stable triples with rk(E1) = rk(E2) = 2, using the theory of mixed Hodge structures (in the cases
that they are smooth and compact). This gives in particular the Poincar´e polynomials of these moduli spaces. As a byproduct, we also give the Hodge polynomial of the moduli space of even degree rank 2 stable vector bundles.