Eduard Looijenga

activity

20242026

collaborators

6 papers

math.AG2026

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…

math.AG2026

Level structures on cyclic covers of $P^{n}$ and the homology of Fermat hypersurfaces

Eduard Looijenga

Let $Z^{'} \subset P^{n}$ be a smooth projective hypersurface of degree $d > 1$ and let $Z \to P^{n}$ be the $I^¼_{d}$ -cover totally ramified along $Z^{'}$ . We relate full level…

math.AG2025

Bidifferentials, Lagrangian projections and the Virasoro extension

Eduard Looijenga

Let $C$ be a smooth projective curve over an algebraically closed field $k$ of characteristic zero. We prove that a Lagrangian supplement of $H^{0} (C, I^c ◯_{C})$ in the de Rham cohomolog…

math.GT2025

The smooth Mordell-Weil group and mapping class groups of elliptic surfaces

Benson Farb, Eduard Looijenga

This is a paper in smooth $4$ -manifold topology, inspired by the NÃ©ron-Lang Theorem in number theory. More precisely, we prove that a smooth version $\MW(Ï)$ of Mordell-Weil grou…

math.GT2025

The configuration functor of a punctured space

Eduard Looijenga, Andreas Stavrou

Let $U$ be a space whose one point compactification $U^{*}$ is a CW-complex for which the added point $*$ is the only $0$ -cell. We observe that the configuration space $C o n f_{n} (U)$ of…

math.AG2024

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…

Hodge decomposition of L_2-cohomology and intersection cohomology of a Shimura variety

Level structures on cyclic covers of Pn and the homology of Fermat hypersurfaces

Bidifferentials, Lagrangian projections and the Virasoro extension

The smooth Mordell-Weil group and mapping class groups of elliptic surfaces

The configuration functor of a punctured space

Cubic threefolds moduli and the Monster group

Level structures on cyclic covers of $P^{n}$ and the homology of Fermat hypersurfaces