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Geometric Perspective on Piecewise Polynomiality of Double Hurwitz Numbers

Published online by Cambridge University Press:  20 November 2018

Renzo Cavalieri  and
Steffen Marcus
Renzo Cavalieri
Affiliation:
Colorado State University, Department of Mathematics, Weber Building, Fort Collins, CO 80523, U.S.A e-mail: renzo@math.colostate.edu
Steffen Marcus
Affiliation:
Department of Mathematics, University of Utah, E Room 233, Salt Lake City, UT 84112, U.S.A e-mail: marcus@math.utah.edu
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Abstract

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We describe double Hurwitz numbers as intersection numbers on the moduli space of curves ${{\overline{M}}_{g,n}}$ Using a result on the polynomiality of intersection numbers of psi classes with the Double Ramification Cycle, our formula explains the polynomiality in chambers of double Hurwitz numbers and the wall-crossing phenomenon in terms of a variation of correction terms to the $\varphi$ classes. We interpret this as suggestive evidence for polynomiality of the Double Ramification Cycle (which is only known in genera 0 and 1).

Keywords

14N35double Hurwitz numberswall crossingsmoduli spacesELSV formula
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 57 , Issue 4 , 01 December 2014 , pp. 749 - 764
Copyright
Copyright © Canadian Mathematical Society 2014

References

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