caa a22 4500 445855630 CHVBK 20180317145427.0 cr unu---uuuuu 170323e20110901xx s 000 0 eng 10.1007/s00026-011-0102-9 doi (NATIONALLICENCE)springer-10.1007/s00026-011-0102-9 The Moduli Space of Curves, Double Hurwitz Numbers, and Faber's Intersection Number Conjecture [Elektronische Daten] [I. Goulden, D. Jackson, R. 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 $${{\mathbb{P}_1}}$$ with given ramification over ∞ and sufficiently many fixed ramification points elsewhere. Degeneration of the target and judicious localization expresses such classes in terms of localization trees weighted by "top intersections” of tautological classes and genus 0 double Hurwitz numbers. This identity of generating series can be inverted, yielding a "combinatorialization” of top intersections of $${\Psi}$$ -classes. As genus 0 double Hurwitz numbers with at most 3 parts over ∞ are well understood, we obtain Faber's Intersection Number Conjecture for up to 3 parts, and an approach to the Conjecture in general (bypassing the Virasoro Conjecture). We also recover other geometric results in a unified manner, including Looijenga's theorem, the socle theorem for curves with rational tails, and the hyperelliptic locus in terms of κ g-2. Springer Basel AG, 2011 moduli space of curves nationallicence branched covers nationallicence Chow rings nationallicence enumerative geometry nationallicence Goulden I. Department of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada aut Jackson D. Department of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada aut Vakil R. Department of Mathematics, Stanford University, 450 Serra Mall, 94305, Stanford, CA, USA aut Annals of Combinatorics SP Birkhäuser Verlag Basel 15/3(2011-09-01), 381-436 0218-0006 15:3<381 2011 15 26 https://doi.org/10.1007/s00026-011-0102-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00026-011-0102-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Goulden I. Department of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada aut NATIONALLICENCE 700 1- Jackson D. Department of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada aut NATIONALLICENCE 700 1- Vakil R. Department of Mathematics, Stanford University, 450 Serra Mall, 94305, Stanford, CA, USA aut NATIONALLICENCE 773 0- Annals of Combinatorics SP Birkhäuser Verlag Basel 15/3(2011-09-01), 381-436 0218-0006 15:3<381 2011 15 26 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer