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

0,3

Comments

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

Links

Table of n, a(n) for n=0..8.

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))

Example

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

Crossrefs

Cf. A007827.

Sequence in context: A048862 A208943 A209071 * A278571 A133669 A205340

Adjacent sequences: A174221 A174222 A174223 * A174225 A174226 A174227

Keyword

nonn,more,hard

Author

_Stefano Maggiolo_, Nov 27 2010

Status

approved