Mirror symmetry and

Author:
Nobuyoshi Takahashi

Journal:
Proc. Amer. Math. Soc. **129** (2001), 29-36

MSC (2000):
Primary 14N10; Secondary 05A15, 20B30

DOI:
https://doi.org/10.1090/S0002-9939-00-05901-3

Published electronically:
September 14, 2000

MathSciNet review:
1784014

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

We show that counting functions of covers of are equal to sums of integrals associated to certain `Feynman' graphs. This is an analogue of the mirror symmetry for elliptic curves.

**[D]**Robbert Dijkgraaf,*Mirror symmetry and elliptic curves*, The moduli space of curves (Texel Island, 1994) Progr. Math., vol. 129, Birkhäuser Boston, Boston, MA, 1995, pp. 149–163. MR**1363055**, https://doi.org/10.1007/978-1-4612-4264-2_5**[GJ1]**I. P. Goulden and D. M. Jackson,*A proof of a conjecture for the number of ramified coverings of the sphere by the torus*, J. Combin. Theory Ser. A**88**(1999), no. 2, 246-258. CMP**2000:04****[GJ2]**I. P. Goulden and D. M. Jackson,*The number of ramified coverings of the sphere by the double torus, and a general form for higher genera*, J. Combin. Theory Ser. A**88**(1999), no. 2, 259-275. CMP**2000:04****[O]**A. Okounkov,*Toda equations for Hurwitz numbers*, preprint (math.AG/0004128).**[SSV]**B. Shapiro, M. Shapiro and A. Vainshtein,*Ramified coverings of with one degenerate branching point and enumeration of edge-ordered graphs*, Topics in Singularity Theory (A. Khovanski, A. Varchenko and V. Vassiliev eds.), Amer. Math. Soc. Transl. (2)**180**AMS (1997), 219-228.**[T1]**N. Takahashi,*Curves in the complement of a smooth plane cubic whose normalizations are*, preprint(alg-geom/9605007).**[T2]**N. Takahashi,*Log mirror symmetry and local mirror symmetry*, to appar in Commun. Math. Phys.**[V]**R. Vakil,*Recursions, formulas, and graph-theoretic interpretations of ramified coverings of the sphere by surfaces of genus 0 and 1*, preprint(math.CO/9812105).

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Additional Information

**Nobuyoshi Takahashi**

Affiliation:
Department of Mathematics, Hiroshima University, Higashi-Hiroshima 739-8526, Japan

Email:
takahasi@math.sci.hiroshima-u.ac.jp

DOI:
https://doi.org/10.1090/S0002-9939-00-05901-3

Received by editor(s):
March 15, 1999

Published electronically:
September 14, 2000

Communicated by:
Ron Donagi

Article copyright:
© Copyright 2000
American Mathematical Society