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The moduli space of cubic surfaces and its orbifold fundamental group
Daniel Allcock, Tathagata Basak, Eduard Looijenga
We find a new presentation of the orbifold fundamental group of the moduli space of cubic surfaces, based on the Artin group of the Petersen graph. This group has two well-known qu…
Level structures on cyclic covers of and the homology of Fermat hypersurfaces
Eduard Looijenga
Let be a smooth projective hypersurface of degree and let be the -cover totally ramified along . We relate full level…
Bidifferentials, Lagrangian projections and the Virasoro extension
Eduard Looijenga
Let be a smooth projective curve over an algebraically closed field of characteristic zero. We prove that a Lagrangian supplement of in the de Rham cohomology…
Hodge decomposition of L_2-cohomology and intersection cohomology of a Shimura variety
Eduard Looijenga
Classical Hodge theory endows the square integrable cohomology of a Shimura variety X with values in a locally homogeneous polarized variation of Hodge structure E with a natural H…
On the motivic description of truncated fundamental group rings
Eduard Looijenga
A topological theorem that appears in a paper by Deligne-Goncharov (and which they attribute to Beilinson) states the following. Let be a path connected pointed space with…
Cubic threefolds moduli and the Monster group
Eduard Looijenga
Allcock constructed a 13-dimensional complex ball quotient of which he conjectured that it admits a natural covering with covering group isomorphic to the Bimonster. This ball quot…
The Hodge polynomial of \Mbar_{3,1}
E. Getzler, E. Looijenga
We give formulas for the Dolbeault numbers of \Mbar_{3,1}, using the first author's calculations of the weights of the cohomology of M_{2,2} and M_{2,3} and the second author's cal…