The reflective modular forms of orthogonal type are fundamental automorphic objects
generalizing the classical Dedekind eta-function. This article describes two methods for …

Abstract We prove the Noether-Lefschetz conjecture on the moduli space of quasi-polarized
K3 surfaces. This is deduced as a particular case of a general theorem that states that low …

We study algebraic cycles on moduli spaces F h of h-polarized hyper-Kähler manifolds.
Following previous work of Marian, Oprea, and Pandharipande on the tautological …

Rigid meromorphic cocycles are defined in the setting of orthogonal groups of arbitrary real
signature and constructed in some instances via a $ p $-adic analogue of Borcherds' …

We determine the behavior of automorphic Green functions along the boundary components
of toroidal compactifications of orthogonal Shimura varieties. We use this analysis to define …

An even lattice of signature is called-reflective if there is a non-constant modular form for the
orthogonal group of, which vanishes only on quadratic divisors orthogonal to-roots of. In …

We prove some new structure results for automorphic products of singular weight. First, we
give a simple characterisation of the Borcherds function. Second, we show that holomorphic …

Quasi‐pullback of Borcherds products is an operation of renormalized restriction. It produces
a meromorphic modular form on a lower dimensional symmetric domain which is again a …

A bstract We reexamine the question of quantum consistency of supergravities in eight
dimensions. Theories with 16 supercharges suffer from the anomalies under the action of its …

We prove a necessary and sufficient condition for the graded algebra of automorphic forms
on a symmetric domain of type IV being free. From the necessary condition, we derive a …