10 papers
Modularity of special cycles on Shimura varieties: a survey
François Greer, Salim Tayou
We survey recent results on a conjecture of Kudla regarding the modularity of generating series of special cycle classes in toroidal compactifications of orthogonal and unitary Shi…
Failure of the invariant cycle theorem over
Donu Arapura, François Greer, Yilong Zhang
We initiate a study of the local invariant cycle theorem with integral coefficients for 1-parameter semistable families of varieties. We show that it always holds for , and it…
The cohomological Kudla conjecture for unitary Shimura varieties
François Greer, Salim Tayou
We construct natural extensions of the Kudla--Millson generating series of cohomology classes of special cycles in compactified unitary Shimura varieties of signature and…
Boundedness of some fibered K-trivial varieties
Philip Engel, Stefano Filipazzi, François Greer +2
We prove that irreducible Calabi-Yau varieties of a fixed dimension, admitting a fibration by abelian varieties or primitive symplectic varieties of a fixed analytic deformation cl…
Modularity of -elliptic loci with level structure
François Greer, Carl Lian, Naomi Sweeting
We consider the generating series of special cycles on , with full level structure, valued in the cohomology of degree . The modula…
Elliptic-elliptic surfaces and the Hesse pencil
François Greer, Yilong Zhang
We construct a family of elliptic surfaces with that arise from base change of the Hesse pencil. We identify explicitly a component of the higher Noether-Lefschetz locus…
-elliptic loci and the Torelli map
François Greer, Carl Lian
We show that two natural cycle classes on the moduli space of compact type stable maps to a varying elliptic curve agree. The first is the virtual fundamental class from Gromov-Wit…
Severi curves of rational elliptic surfaces
François Greer, Joseph Helfer, John Sheridan
We study Severi curves parametrizing rational bisections of elliptic fibrations associated to general pencils of plane cubics. Our main results show that these Severi curves are co…
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…
Quasi-modular forms from mixed Noether-Lefschetz theory
François Greer
The Gromov-Witten theory of threefolds admitting a smooth K3 fibration can be solved in terms of the Noether-Lefschetz intersection numbers of the fibration and the reduced invaria…