7 papers
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…
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…
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…
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…
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…