1 citations · 1 across the 7 of their papers we have counts for
11 papers
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…
Extremal mappings of tori, Teichmüller potentials and symmetric-space distance
Benson Farb, Eduard Looijenga
The symmetric space $X_n={\rm SL}(n,\Rb)/{\rm SO}(n)$ can be interpreted as the Teichmüller space of marked, unit volume, flat -dimensional tori. It comes with a unique (up to s…
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…
The configuration functor of a punctured space
Eduard Looijenga, Andreas Stavrou
Let be a space whose one point compactification is a CW-complex for which the added point is the only -cell. We observe that the configuration space of…
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…
The smooth Mordell-Weil group and mapping class groups of elliptic surfaces
Benson Farb, Eduard Looijenga
This is a paper in smooth -manifold topology, inspired by the Néron-Lang Theorem in number theory. More precisely, we prove that a smooth version $\MW(π)$ of Mordell-Weil group…
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…
Connectivity of complexes of separating curves
Eduard Looijenga
We prove that the separated curve complex of a closed orientable surface of genus g is (g-3)-connected. We also obtain a connectivity property for a separated curve complex of the…
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…