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Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Rational curves on prime Fano threefolds of index 1

Authors: Brian Lehmann and Sho Tanimoto
Journal: J. Algebraic Geom. 30 (2021), 151-188
Published electronically: December 9, 2019
MathSciNet review: 4233180
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Abstract | References | Additional Information

Abstract: We study the moduli spaces of rational curves on prime Fano threefolds of index 1. For general threefolds of most genera we compute the dimension and the number of irreducible components of these moduli spaces. Our results confirm Geometric Manin’s Conjecture in these examples and show the enumerativity of certain Gromov-Witten invariants.

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Additional Information

Brian Lehmann
Affiliation: Department of Mathematics, Boston College, Chestnut Hill, Massachusetts 02467
MR Author ID: 977848

Sho Tanimoto
Affiliation: Department of Mathematics, Faculty of Science, Kumamoto University, Kurokami 2-39-1, Kumamoto 860-8555, Japan
MR Author ID: 973697

Received by editor(s): August 15, 2018
Received by editor(s) in revised form: September 6, 2018, and July 16, 2019
Published electronically: December 9, 2019
Additional Notes: The first author was supported by NSF grant 1600875. The second author was partially supported by Lars Hesselholt’s Niels Bohr professorship and by MEXT Japan, Leading Initiative for Excellent Young Researchers (LEADER), Inamori Foundation, and JSPS KAKENHI Early-Career Scientists Grant number 19K14512.
Article copyright: © Copyright 2019 University Press, Inc.