18 citations · 32 across the 7 of their papers we have counts for
13 papers · 1 filter
The projective invariants of ordered points on the line
Benjamin J. Howard, John Millson, Andrew Snowden +1
The space of n (ordered) points on the projective line, modulo automorphisms of the line, is one of the most important and classical examples of an invariant theory quotient, and i…
Murphy's Law in algebraic geometry: Badly-behaved deformation spaces
Ravi Vakil
We consider the question: ``How bad can the deformation space of an object be?'' The answer seems to be: ``Unless there is some a priori reason otherwise, the deformation space may…
The affine stratification number and the moduli space of curves
Mike Roth, Ravi Vakil
We define the affine stratification number asn X of a scheme X. For X equidimensional, it is the minimal number k such that there is a stratification of X by locally closed affine…
Towards the geometry of double Hurwitz numbers
Ian Goulden, David Jackson, Ravi Vakil
Double Hurwitz numbers count branched covers of the projective line with fixed branch points, with simple branching required over all but two points 0 and infinity, and the branchi…
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…
A geometric Littlewood-Richardson rule
Ravi Vakil
We describe an explicit geometric Littlewood-Richardson rule, interpreted as deforming the intersection of two Schubert varieties so that they break into Schubert varieties. There…