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8 papers · 1 filter
The birational geometry of moduli of cubic surfaces and cubic surfaces with a line
Sebastian Casalaina-Martin, Samuel Grushevsky, Klaus Hulek
We determine the cones of effective and nef divisors on the toroidal compactification of the ball quotient model of the moduli space of complex cubic surfaces with a chosen line. F…
A tale of two moduli spaces: logarithmic and multi-scale differentials
Dawei Chen, Samuel Grushevsky, David Holmes +2
Multi-scale differentials were constructed by M.~Bainbridge, D.~Chen, Q.~Gendron, S.~Grushevsky, and M.~Möller, from the viewpoint of flat and complex geometry, for the purpose of…
Non-isomorphic smooth compactifications of the moduli space of cubic surfaces
Sebastian Casalaina-Martin, Samuel Grushevsky, Klaus Hulek +1
The moduli space of complex cubic surfaces has three different, but isomorphic, compact realizations: as a GIT quotient, as a Baily--Borel compactification of a ball quotient, and…
Modular forms from Noether-Lefschetz theory
François Greer
We enumerate smooth rational curves on very general Weierstrass fibrations over hypersurfaces in projective space. The generating functions for these numbers lie in the ring of cla…
Nef cones of nested Hilbert schemes of points on surfaces
Tim Ryan, Ruijie Yang
Let be the projective plane, a Hirzebruch surface, or a general surface. In this paper, we study the birational geometry of various nested Hilbert schemes of points parame…
The Effective Cone of Moduli Spaces of Sheaves on a Smooth Quadric Surface
Tim Ryan
Let be a stable Chern character on , and let be the moduli space of Gieseker semistable sheaves on w…