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Abstract: To the integral symplectic group Sp2g,Z we associate two posets of which weprove that they have the Cohen-Macaulay property. As an application we showthat the locus of marked decomposable principally polarized abelian varietiesin the Siegel space of genus g has the homotopy type of a bouquet ofg-2-spheres. This, in turn, implies that the rational homology of modulispace of unmarked principal polarized abelian varieties of genus g modulo thedecomposable ones vanishes in degree g-2 or lower. Another application is animproved stability range for the homology of the symplectic groups overEuclidean rings. But the original motivation comes from envisaged applicationsto the homology of groups of Torelli type.The proof of our main result rests on a refined nerve theorem for posets thatmay have an interest in its own right.



Autor: Wilberd van der Kallen, Eduard Looijenga

Fuente: https://arxiv.org/



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