Counting elliptic plane curves

with fixed -invariant

Author:
Rahul Pandharipande

Journal:
Proc. Amer. Math. Soc. **125** (1997), 3471-3479

MSC (1991):
Primary 14N10, 14H10; Secondary 14E99

MathSciNet review:
1423328

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Abstract | References | Similar Articles | Additional Information

Abstract: The number of degree elliptic plane curves with fixed -invariant passing through general points in is computed.

**[A]**V. Alexeev,*Moduli spaces for Surfaces*, preprint 1994.**[Al]**Paolo Aluffi,*How many smooth plane cubics with given 𝑗-invariant are tangent to 8 lines in general position?*, Enumerative algebraic geometry (Copenhagen, 1989) Contemp. Math., vol. 123, Amer. Math. Soc., Providence, RI, 1991, pp. 15–29. MR**1143545**, 10.1090/conm/123/1143545**[B-M]**K. Behrend and Yu. Manin,*Stacks of stable maps and Gromov-Witten invariants*, Duke Math. J.**85**(1996), 1-60.**[F-P]**W. Fulton and R. Pandharipande,*Notes on stable maps and quantum cohomology*, Proc. Amer. Math. Soc. (to appear).**[DF-I]**P. Di Francesco and C. Itzykson,*Quantum intersection rings*, The moduli space of curves (Texel Island, 1994) Progr. Math., vol. 129, Birkhäuser Boston, Boston, MA, 1995, pp. 81–148. MR**1363054****[I]**E.-M. Ionel, Michigan State University Ph.D. thesis, (1996).**[K-Q-R]**S. Katz, Z. Qin, and Y. Ruan,*Composition law and nodal genus-2 curves in*, preprint 1996.**[K]**Maxim Kontsevich,*Enumeration of rational curves via torus actions*, The moduli space of curves (Texel Island, 1994) Progr. Math., vol. 129, Birkhäuser Boston, Boston, MA, 1995, pp. 335–368. MR**1363062****[K-M]**M. Kontsevich and Yu. Manin,*Gromov-Witten classes, quantum cohomology, and enumerative geometry*, Comm. Math. Phys.**164**(1994), no. 3, 525–562. MR**1291244****[R-T]**Y. Ruan and G. Tian,*A mathematical theory of quantum cohomology*, J. Diff. Geom.**42**(1995), 259-367.

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Additional Information

**Rahul Pandharipande**

Affiliation:
Department of Mathematics, University of Chicago, Chicago, Illinois 60637

Email:
rahul@math.uchicago.edu

DOI:
https://doi.org/10.1090/S0002-9939-97-04136-1

Keywords:
Gromov-Witten invariants,
elliptic curves,
enumerative geometry

Received by editor(s):
June 19, 1996

Additional Notes:
Partially supported by an NSF Post-Doctoral Fellowship

Communicated by:
Ron Donagi

Article copyright:
© Copyright 1997
American Mathematical Society