caa a22 4500 445884584 CHVBK 20180317145555.0 cr unu---uuuuu 170323e20110601xx s 000 0 eng 10.1007/s10711-010-9553-0 doi (NATIONALLICENCE)springer-10.1007/s10711-010-9553-0 Spherical complexes attached to symplectic lattices [Elektronische Daten] [Wilberd van der Kallen, Eduard Looijenga] To the integral symplectic group $${{\rm Sp}(2g,\mathbb{Z})}$$ we associate two posets of which we prove that they have the Cohen-Macaulay property. As an application we show that the locus of marked decomposable principally polarized abelian varieties in the Siegel space of genus g has the homotopy type of a bouquet of (g − 2)-spheres. This, in turn, implies that the rational homology of moduli space of (unmarked) principal polarized abelian varieties of genus g modulo the decomposable ones vanishes in degree ≤ g − 2. Another application is an improved stability range for the homology of the symplectic groups over Euclidean rings. But the original motivation comes from envisaged applications to the homology of groups of Torelli type. The proof of our main result rests on a refined nerve theorem for posets that may have an interest in its own right. The Author(s), 2010 Integral symplectic group nationallicence Cohen-Macaulay poset nationallicence van der Kallen Wilberd Mathematisch Instituut, Universiteit Utrecht, P.O. Box 80.010, 3508 TA, Utrecht, The Netherlands aut Looijenga Eduard Mathematisch Instituut, Universiteit Utrecht, P.O. Box 80.010, 3508 TA, Utrecht, The Netherlands aut Geometriae Dedicata Springer Netherlands 152/1(2011-06-01), 197-211 0046-5755 152:1<197 2011 152 10711 https://doi.org/10.1007/s10711-010-9553-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10711-010-9553-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- van der Kallen Wilberd Mathematisch Instituut, Universiteit Utrecht, P.O. Box 80.010, 3508 TA, Utrecht, The Netherlands aut NATIONALLICENCE 700 1- Looijenga Eduard Mathematisch Instituut, Universiteit Utrecht, P.O. Box 80.010, 3508 TA, Utrecht, The Netherlands aut NATIONALLICENCE 773 0- Geometriae Dedicata Springer Netherlands 152/1(2011-06-01), 197-211 0046-5755 152:1<197 2011 152 10711 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer