6 papers · 1 filter
Polync varieties and multiparameter Kulikov models
Philip Engel
We study "polync varieties", whose singularities are locally products of normal crossing (nc) singularities. We introduce the notion of d-semistability of such varieties, and gener…
On the non-abelian Hodge locus I
Philip Engel, Salim Tayou
We partially resolve conjectures of Deligne and Simpson concerning -local systems on quasi-projective varieties that underlie a polarized variation of Hodge structure.…
On lattice-polarized K3 surfaces
Valery Alexeev, Philip Engel
We propose modifications to the commonly used definitions of lattice-polarized and lattice-quasipolarized smooth K3 surfaces, collecting various versions of the definition, and det…
Shafarevich's conjecture for families of hypersurfaces over function fields
Philip Engel, Alice Lin, Salim Tayou
Given a smooth quasi-projective complex algebraic variety , we prove that there are only finitely many Hodge-generic non-isotrivial families of smooth projective hyper…
Mixed mock modularity of special divisors
Philip Engel, François Greer, Salim Tayou
We prove that the generating series of special divisors in toroidal compactifications of orthogonal Shimura varieties is a mixed mock modular form. More precisely, we find an expli…
Periods of elliptic surfaces with
Philip Engel, François Greer, Abigail Ward
We prove that the period mapping is dominant for elliptic surfaces over an elliptic curve with 12 nodal fibers, and that its degree is larger than 1.