Degenerations of surface scrolls and the Gromov-Witten invariants of Grassmannians
Author:
Izzet Coskun
Journal:
J. Algebraic Geom. 15 (2006), 223-284
DOI:
https://doi.org/10.1090/S1056-3911-06-00426-7
Published electronically:
January 11, 2006
MathSciNet review:
2199064
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Abstract |
References |
Additional Information
Abstract: We describe an algorithm for computing certain characteristic numbers of rational normal surface scrolls using degenerations. As a corollary we obtain an efficient method for computing the corresponding Gromov-Witten invariants of the Grassmannians of lines.
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[BKT]buch:doodle A. S. Buch, A. Kresch, and H. Tamvakis. Gromov-Witten invariants on Grassmannians. J. Amer. Math. Soc. 16 (2003), 901–915.
[CH]Capharris:severi L. Caporaso and J. Harris. Counting plane curves of any genus. Invent. Math. 131 no.2 (1998), 345–392.
[Ci]ciocan:flag I. Ciocan-Fontanine. On quantum cohomology rings of partial flag varieties. Duke Math. J. 98 (1999), 485–524.
[C1]coskun3:degenerations I. Coskun. Degenerations of Rational Normal Scrolls and the Gromov-Witten invariants of Grassmannians. in preparation.
[C2]coskun2:degenerations I. Coskun. The enumerative geometry of Del Pezzo surfaces via degenerations. to appear in Amer. J. Math.
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[V3]vakil:thesis R. Vakil. The enumerative geometry of rational and elliptic curves in projective space. Thesis Harvard University, alg-geom/9709007.
Additional Information
Izzet Coskun
Affiliation:
Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138
Address at time of publication:
Department of Mathematics, M.I.T., Cambridge, Massachusetts 02139
MR Author ID:
736580
Email:
coskun@math.harvard.edu, coskun@math.mit.edu
Received by editor(s):
February 23, 2004
Received by editor(s) in revised form:
September 19, 2004, February 26, 2005, and August 22, 2005
Published electronically:
January 11, 2006
