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A short proof of the λg-conjecture without Gromov-Witten theory: Hurwitz theory and the moduli of curves
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I. P. Goulden
Published/Copyright:
November 23, 2009
Abstract
We give a short and direct proof of Getzler and Pandharipande's λg-conjecture. The approach is through the Ekedahl-Lando-Shapiro-Vainshtein theorem, which establishes the “polynomiality” of Hurwitz numbers, from which we pick off the lowest degree terms. The proof is independent of Gromov-Witten theory.
We briefly describe the philosophy behind our general approach to intersection numbers and how it may be extended to other intersection number conjectures. Ideas from this paper feature in two independent recent enlightening proofs of Witten's conjecture by Kazarian [Adv. Math.] and Chen, Li, and Liu [Asian J. Math. 12: 511–518, 2009].
Received: 2006-05-26
Revised: 2008-07-15
Published Online: 2009-11-23
Published in Print: 2009-December
© Walter de Gruyter Berlin · New York 2009
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Articles in the same Issue
- Trees and mapping class groups
- The Hartogs extension theorem on (n – 1)-complete complex spaces
- On Hartogs' extension theorem on (n – 1)-complete complex spaces
- Cohomological finiteness conditions for elementary amenable groups
- The behaviour of the differential Galois group on the generic and special fibres: A Tannakian approach
- Discrete holomorphic geometry I. Darboux transformations and spectral curves
- Multilinear morphisms between 1-motives
- A short proof of the λg-conjecture without Gromov-Witten theory: Hurwitz theory and the moduli of curves
- Unobstructedness of deformations of holomorphic maps onto Fano manifolds of Picard number 1
- Cayley decompositions of lattice polytopes and upper bounds for h*-polynomials
- Siegel's trace problem and character values of finite groups
