Eduard Looijenga

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20242026

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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.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

Cubic threefolds moduli and the Monster group

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