A174224 Number of homeomorphism classes of stable curves in the moduli space of stable curves of genus g.

0, 0, 7, 42, 379, 4555, 69808, 1281678, 27297406

Offset: 0

Author

Stefano Maggiolo, Nov 27 2010

Keywords

• nonn
• more
• hard

Comments

a(g) is also the number of stable graphs of type (g,0) (see reference).

Examples

			a(0) = a(1) = 0 because there are no stable curves of genus 0 or 1.
		

Links

• Melody T. Chan, Tropical curves and metric graphs, Ph. D. Dissertation, Univ. Calif. Berkeley, Spring 2012.
• Melody Chan, Combinatorics of the tropical Torelli map, Algebra Number Theory, 6 (2012), 1133-1169.
• Melody Chan, Graph complexes and the top-weight Euler characteristic of M_(g,n), Lecture Notes, Brown University (2020).
• Pierre Deligne and David Mumford, The irreducibility of the space of curves of given genus, Inst. Hautes Études Sci. Publ. Math. No. 36, 1969, 75-109.
• Stefano Maggiolo and Nicola Pagani, Boundary graph computer for the moduli space of stable pointed curves (includes program to compute a(n)).

Crossrefs

Cf. A007827.

Row sums of triangle A366039.