34 citations · 41 across the 3 of their papers we have counts for
8 papers · 1 filter
Relative virtual localization and vanishing of tautological classes on moduli spaces of curves
Tom Graber, Ravi Vakil
We prove a localization formula for the moduli space of stable relative maps. As an application, we prove that all codimension i tautological classes on the moduli space of stable…
Rational connectivity and sections of families over curves
T. Graber, J. Harris, B. Mazur +1
We show that if a family of complex varieties over a base B admits a section when restricted to a very general curve in B, then the family must contain a subfamily of rationally co…
A note on Hurwitz schemes of covers of a positive genus curve
Tom Graber, Joe Harris, Jason Starr
We prove the irreducibility of the space parametrizing branched covers of a fixed Riemann surface of degree , with at least 2d branch points, and with monodromy group equal…
Algebraic orbifold quantum products
Dan Abramovich, Tom Graber, Angelo Vistoli
The purpose of this note is to give an overview of our work on defining algebraic counterparts for W. Chen and Y. Ruan's Gromov-Witten Theory of orbifolds. This work will be descri…
Families of rationally connected varieties
Tom Graber, Joe Harris, Jason Starr
We prove that a one-parameter family of rationally connected varieties (over an algebraically closed field of characteristic 0) always has a section.
On the tautological ring of
T. Graber, R. Vakil
We prove that the dimension 0 part of the tautological ring of the moduli space of stable pointed curves is one-dimensional. This provides the first genus-free evidence for a conje…