The Siegel Modular Variety of Degree Two and Level Four - Rilegato

Lee, Ronnie; Weintraub, Steven H.; Hoffman, Jerome William

Rilegato

ISBN 10: 0821806203 ISBN 13: 9780821806203

Casa editrice: Amer Mathematical Society, 1998

Riassunto

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 $\mathbfM_4$.

Dettagli dell?edizione

• Editore: Amer Mathematical Society
• Data di pubblicazione: 1998
• Lingua: Inglese
• ISBN 10: 0821806203
• ISBN 13: 9780821806203
• Rilegatura: Copertina rigida
• Numero di pagine: 75
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile