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Towards the geometry of double Hurwitz numbers

- I. Goulden, D. Jackson, R. Vakil
- Mathematics
- 27 September 2003

Abstract Double Hurwitz numbers count branched covers of CP 1 with fixed branch points, with simple branching required over all but two points 0 and ∞ , and the branching over 0 and ∞ specified by… Expand

Relative virtual localization and vanishing of tautological classes on moduli spaces of curves

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 pointed curves… Expand

Counting curves on rational surfaces

- R. Vakil
- Mathematics
- 21 May 2000

Abstract:In [CH3], Caporaso and Harris derive recursive formulas counting nodal plane curves of degree d and geometric genus g in the plane (through the appropriate number of fixed general points).… Expand

Murphy’s law in algebraic geometry: Badly-behaved deformation spaces

- R. Vakil
- Mathematics
- 22 November 2004

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 be as bad as… Expand

Discriminants in the Grothendieck Ring

We consider the "limiting behavior" of *discriminants*, by which we mean informally the locus in some parameter space of some type of object where the objects have certain singularities. We focus on… Expand

A geometric Littlewood-Richardson rule

- R. Vakil
- Mathematics
- 24 February 2003

We describe a geometric Littlewood-Richardson rule, interpreted as deforming the intersection of two Schubert varieties into the union of Schubert varieties. There are no restrictions on the base… Expand

A desingularization of the main component of the moduli space of genus-one stable maps into ℙn

We construct a natural smooth compactification of the space of smooth genus-one curves with k distinct points in a projective space. It can be viewed as an analogue of a well-known smooth… Expand

On Conway's recursive sequence

TLDR

Schubert induction

- R. Vakil
- Mathematics
- 25 February 2003

We describe a Schubert induction theorem, a tool for analyzing intersections on a Grassmannian over an arbitrary base ring. The key ingredient in the proof is the Geometric Littlewood-Richardson rule… Expand

Twelve points on the projective line, branched covers, and rational elliptic fibrations

- R. Vakil
- Mathematics
- 14 October 1999

Abstract. The following divisors in the space
${\rm Sym}^{12}{\mathbb P}^1$ of twelve points on
${\mathbb P}^1$ are actually the same:
$({\mathcal A})$ the possible locus of the twelve nodal… Expand

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