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The Geometry and Arithmetic of Maschke's Calabi-Yau threefold
Bert Van Geemen (Università di Milano) Maschke's Calabi-Yau threefold is the double cover of projective three space branched along Maschke's octic surface. This surface is defined by the lowest degree invariant of a certain finite group acting on a four dimensional vector space. Using this group, we show that the middle Betti cohomology group of the threefold decomposes into the direct sum of 150 two-dimensional Hodge substructures. We exhibit one dimensional families of rational curves on the threefold and verify that the associated Abel-Jacobi map is non-trivial. We also discuss the modularity of the Galois representations associated to Maschke's threefold, as proven recently by M. Schuett. |  |
Organizing committee: Alberto Albano, Elisabetta Ambrogio, Ernesto Buzano, Giuseppe Ceresa, Federica Galluzzi, Marina Marchisio, Claudio Pedrini, Daniela Romagnoli, Alessandro Verra, Giuseppe Vigna Suria