scholarly journals A Conjectural Description of the Tautological Ring of the Moduli Space of Curves

1999 ◽  
pp. 109-129 ◽  
Author(s):  
Carel Faber
Keyword(s):  
Moduli Space ◽  
Moduli Space Of Curves ◽  
Tautological Ring

scholarly journals Relations in the tautological ring of the moduli space of curves

2021 ◽  
Vol 17 (2) ◽  
pp. 717-771
Author(s):  
R. Pandharipande ◽  
A. Pixton
Keyword(s):  
Moduli Space ◽  
Moduli Space Of Curves ◽  
Tautological Ring

Relations in the tautological ring derived from combinatorial classes and hyperelliptic fatgraphs

2008 ◽  
Vol 144 (2) ◽  
pp. 369-395
Author(s):  
ALEX JAMES BENE
Keyword(s):  
Moduli Space ◽  
Cell Decomposition ◽  
Integration Scheme ◽  
Weighted Sum ◽  
Closed Formula ◽  
Moduli Space Of Curves ◽  
Hodge Integrals ◽  
Tautological Ring ◽  
Level Intersection ◽  
Chain Level

AbstractA closed formula is obtained for the integral$\int_{\Hgbs^1}\kappa_{1}\psi^{2g-2}$of tautological classes over the locus of hyperelliptic Weier points in the moduli space of curves. As a corollary, a relation between Hodge integrals is obtained.The calculation utilizes the homeomorphism between the moduli space of curves$\M_{g,1}$and the combinatorial moduli space$\Mc_{g,1}$, a PL-orbifold whose cells are enumerated by fatgraphs. This cell decomposition can be used to naturally construct combinatorial PL-cycles$W_a\subset\Mc_{g,1}$whose homology classes are essentially the Poin duals of the Mumford–Morita–Miller classes κa. In this paper we construct another PL-cycle$\Hgc \subset \Mc_{g,1}$representing the locus of hyperelliptic Weier points and explicitly describe the chain level intersection of this cycle withW1. Using this description of$\Hgc\cap W_1$, the duality between Witten cyclesWaand the κaclasses, and the Kontsevich--Penner method of integration, scheme of integrating ε classes, the integral$\int_{\Hgbs^1}\kappa_{1}\psi^{2g-2}$is reduced to a weighted sum over graphs and is evaluated by the enumeration of trees.

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.

The moduli space of curves of genus two covering elliptic curves

1994 ◽  
Vol 84 (1) ◽  
pp. 125-133 ◽  
Author(s):  
Naoki Murabayashi
Keyword(s):  
Elliptic Curves ◽  
Moduli Space ◽  
Moduli Space Of Curves ◽  
Genus Two
Sign in / Sign up

Export Citation Format

Share Document