The Siegel modular variety of degree two and level four Cohomology of the Siegel modular group of degree two and level four
著者
書誌事項
The Siegel modular variety of degree two and level four . Cohomology of the Siegel modular group of degree two and level four
（Memoirs of the American Mathematical Society, no. 631）
American Mathematical Society, 1998
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注記
"May 1998, volume 133, number 631 (second of 5 numbers)"--T.p
Includes bibliographical references
内容説明・目次
内容説明
The Siegel Modular Variety of Degree Two and Level Four is by Ronnie Lee and Steven H. Weintraub: Let $\mathbf M_n$ denote the quotient of the degree two Siegel space by the principal congruence subgroup of level $n$ of $Sp_4(\mathbb Z)$. $\mathbfM_n$ is the moduli space of principally polarized abelian surfaces with a level $n$ structure and has a compactification $\mathbfM^*_n$ first constructed by Igusa. $\mathbfM^*_n$ is an almost non-singular (non-singular for $n> 1$) complex three-dimensional projective variety (of general type, for $n> 3$). The authors analyze the Hodge structure of $\mathbfM^*_4$, completely determining the Hodge numbers $h^{p,q} = \dim H^{p,q}(\mathbfM^*_4)$. Doing so relies on the understanding of $\mathbfM^*_2$ and exploitation of the regular branched covering $\mathbfM^*_4 \rightarrow \mathbfM^*_2$.""Cohomology of the Siegel Modular Group of Degree Two and Level Four"" is by J. William Hoffman and Steven H. Weintraub. The authors compute the cohomology of the principal congruence subgroup $\Gamma_2(4) \subset S{_p4} (\mathbb Z)$ consisting of matrices $\gamma \equiv \mathbf 1$ mod 4. This is done by computing the cohomology of the moduli space $\mathbfM_4$. The mixed Hodge structure on this cohomology is determined, as well as the intersection cohomology of the Satake compactification of $\mathbfM_4$.
目次
The Siegel Modular Variety of Degree Two and Level Four: Introduction Algebraic background Geometric background Taking stock Type III A Type II A Type II B Type IV C Summing up Appendix. An exact sequence in homology References Cohomology of the Siegel Modular Group of Degree Two and Level Four: Introduction The building Cycles The main theorems References.
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