scholarly journals The Moduli Space of Curves, Double Hurwitz Numbers, and Faber’s Intersection Number Conjecture

2011 ◽  
Vol 15 (3) ◽  
pp. 381-436 ◽  
Author(s):  
I. P. Goulden ◽  
D. M. Jackson ◽  
R. Vakil
Keyword(s):  
Moduli Space ◽  
Intersection Number ◽  
Moduli Space Of Curves ◽  
Hurwitz Numbers

scholarly journals Geometric Perspective on Piecewise Polynomiality of Double Hurwitz Numbers

2014 ◽  
Vol 57 (4) ◽  
pp. 749-764 ◽  
Author(s):  
Renzo Cavalieri ◽  
Steffen Marcus
Keyword(s):  
Moduli Space ◽  
Moduli Space Of Curves ◽  
Intersection Numbers ◽  
Hurwitz Numbers ◽  
Suggestive Evidence ◽  
Wall Crossing ◽  
Double Ramification Cycle ◽  
Correction Terms

AbstractWe describe doubleHurwitz numbers as intersection numbers on the moduli space of curves 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 ψ classes. We interpret this as suggestive evidence for polynomiality of the Double Ramification Cycle (which is only known in genera 0 and 1).

scholarly journals Transitive Factorizations in the Hyperoctahedral Group

2008 ◽  
Vol 60 (2) ◽  
pp. 297-312
Author(s):  
G. Bini ◽  
I. P. Goulden ◽  
D. M. Jackson
Keyword(s):  
Symmetric Group ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Point Of View ◽  
Moduli Space Of Curves ◽  
Reflection Groups ◽  
Hurwitz Numbers ◽  
Hyperoctahedral Group ◽  
Geometric Point ◽  
Enumeration Problem

AbstractThe classical Hurwitz enumeration problem has a presentation in terms of transitive factorizations in the symmetric group. This presentation suggests a generalization from type A to other finite reflection groups and, in particular, to type B. We study this generalization both from a combinatorial and a geometric point of view, with the prospect of providing a means of understanding more of the structure of the moduli spaces of maps with an S2-symmetry. The type A case has been well studied and connects Hurwitz numbers to the moduli space of curves. We conjecture an analogous setting for the type B case that is studied here.

The Kodaira dimension of the moduli space of curves of genus ?23

1987 ◽  
Vol 90 (2) ◽  
pp. 359-387 ◽  
Author(s):  
David Eisenbud ◽  
Joe Harris
Keyword(s):  
Moduli Space ◽  
Kodaira Dimension ◽  
Moduli Space Of Curves

scholarly journals Brill–Noether loci in codimension two

2013 ◽  
Vol 149 (9) ◽  
pp. 1535-1568 ◽  
Author(s):  
Nicola Tarasca
Keyword(s):  
Moduli Space ◽  
Moduli Space Of Curves ◽  
Stable Curves ◽  
Codimension Two

AbstractLet us consider the locus in the moduli space of curves of genus$2k$defined by curves with a pencil of degree$k$. Since the Brill–Noether number is equal to$- 2$, such a locus has codimension two. Using the method of test surfaces, we compute the class of its closure in the moduli space of stable curves.

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