19 citations · 77 across the 19 of their papers we have counts for
6 papers · 2 filters
The moduli space of curves, double Hurwitz numbers, and Faber's intersection number conjecture
Ian P. Goulden, David M. Jackson, Ravi Vakil
We define the dimension 2g-1 Faber-Hurwitz Chow/homology classes on the moduli space of curves, parametrizing curves expressible as branched covers of P^1 with given ramification o…
Geometric positivity in the cohomology of homogeneous spaces and generalized Schubert calculus
Izzet Coskun, Ravi Vakil
We describe recent work on positive descriptions of the structure constants of the cohomology of homogeneous spaces such as the Grassmannian, by degenerations and related methods.…
The moduli space of n points on the line is cut out by simple quadrics when n is not six
Benjamin Howard, John Millson, Andrew Snowden +1
A central question in invariant theory is that of determining the relations among invariants. Geometric invariant theory quotients come with a natural ample line bundle, and hence…
A natural smooth compactification of the space of elliptic curves in projective space
Ravi Vakil, Aleksey Zinger
The space of smooth genus 0 curves in projective space has a natural smooth compactification: the moduli space of stable maps, which may be seen as the generalization of the classi…
A short proof of the lambda_g-conjecture without Gromov-Witten theory: Hurwitz theory and the moduli of curves
Ian P. Goulden, David M. Jackson, Ravi Vakil
We give a short and direct proof of the -Conjecture. The approach is through the Ekedahl-Lando-Shapiro-Vainshtein theorem, which establishes the ``polynomiality'' of Hurwitz n…
The moduli space of curves and Gromov-Witten theory
Ravi Vakil
The goal of this article is to motivate and describe how Gromov-Witten theory can and has provided tools to understand the moduli space of curves. For example, ideas and methods fr…