Counting elliptic plane curves with fixed invariant
Author:
Rahul Pandharipande
Journal:
Proc. Amer. Math. Soc. 125 (1997), 34713479
MSC (1991):
Primary 14N10, 14H10; Secondary 14E99
MathSciNet review:
1423328
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Abstract 
References 
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Additional Information
Abstract: The number of degree elliptic plane curves with fixed invariant passing through general points in is computed.
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 [A]
 V. Alexeev, Moduli spaces for Surfaces, preprint 1994.
 [Al]
 P. Aluffi, How many smooth plane cubics with given invariant are tangent to 8 lines in general position?, Contemporary Mathematics (1991) 1529. MR 93e:14063
 [BM]
 K. Behrend and Yu. Manin, Stacks of stable maps and GromovWitten invariants, Duke Math. J. 85 (1996), 160.
 [FP]
 W. Fulton and R. Pandharipande, Notes on stable maps and quantum cohomology, Proc. Amer. Math. Soc. (to appear).
 [DFI]
 P. Di Francesco and C. Itzykson, Quantum intersection rings, in The moduli space of curves, R. Dijkgraaf, C. Faber, and G. van der Geer, eds., Birkhauser, 1995 pp 81148. MR 96k:14041a
 [I]
 E.M. Ionel, Michigan State University Ph.D. thesis, (1996).
 [KQR]
 S. Katz, Z. Qin, and Y. Ruan, Composition law and nodal genus2 curves in , preprint 1996.
 [K]
 M. Kontsevich, Enumeration of rational curves via torus actions, in The moduli space of curves, R. Dijkgraaf, C. Faber, and G. van der Geer, eds., Birkhauser, 1995 pp 335368. MR 97d:14077
 [KM]
 M. Kontsevich and Y. Manin, GromovWitten classes, quantum cohomology, and enumerative geometry, Commun. Math. Phys. (1994) 525562. MR 95i:14049
 [RT]
 Y. Ruan and G. Tian, A mathematical theory of quantum cohomology, J. Diff. Geom. 42 (1995), 259367.
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Additional Information
Rahul Pandharipande
Affiliation:
Department of Mathematics, University of Chicago, Chicago, Illinois 60637
Email:
rahul@math.uchicago.edu
DOI:
http://dx.doi.org/10.1090/S0002993997041361
PII:
S 00029939(97)041361
Keywords:
GromovWitten invariants,
elliptic curves,
enumerative geometry
Received by editor(s):
June 19, 1996
Additional Notes:
Partially supported by an NSF PostDoctoral Fellowship
Communicated by:
Ron Donagi
Article copyright:
© Copyright 1997 American Mathematical Society
