The rational cohomology ring of the moduli space of abelian 3-folds

By R. Hain. 2002

60 citations recorded by the source corpus.

The rational cohomology ring of A_3, the moduli space of abelian 3-folds is computed. This is isomorphic to the the rational cohomology ring of the group Sp_3(Z) of 6x6 integral symplectic matrices. The main ingredients in the computation are (1) Looijenga's computation of the rational cohomology ring of M_3, the moduli space of smooth projective curves of genus 3, and (2) the stratified Morse theory of Goresky and MacPherson, which we use to compute the homology of the jacobian locus (in the rank 3 Siegel upper half plane), or equivalently of the extended Torelli group in genus 3. In the revised version, we also compute the rational cohomology of the Satake compactification of A_3.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/407f8488de6c3f065eff69d2293900d39c9dcdfd

Citations in the corpus

• Siegel modular forms of degree three and the cohomology of local systems (2011, unknown): “1 true for λ = (0, 0, 0) we put S[0, 0, 4] := L(6) + L(5) + L(4) + 2L(3) + L(2) + L+ 1, because we know that ec(A3,V0,0,0) = L 6 + L5 + L4 + L3 + 1, see [32].”