RATIONAL CURVES ON PRIME FANO THREEFOLDS OF INDEX 1

被引：13
|
作者：
Lehmann, Brian [1 ]
Tanimoto, Sho [2 ]
机构：
[1] Boston Coll, Dept Math, Chestnut Hill, MA 02467 USA
[2] Kumamoto Univ, Fac Sci, Dept Math, Kurokami 2-39-1, Kumamoto 8608555, Japan
来源：
JOURNAL OF ALGEBRAIC GEOMETRY | 2021年 / 30卷 / 01期
基金：
美国国家科学基金会;
关键词：
GROMOV-WITTEN INVARIANTS; BUNDLES;
D O I：
10.1090/jag/751
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
引用
收藏
页码：151 / 188
页数：38
相关论文
共 50 条
  • [21] Q-Fano Threefolds of Index 7
    Prokhorov, Yuri G.
    PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2016, 294 (01) : 139 - 153
  • [22] Rational curves in Calabi-Yau threefolds
    Johnsen, T
    Knutsen, AL
    COMMUNICATIONS IN ALGEBRA, 2003, 31 (08) : 3917 - 3953
  • [23] K-moduli of Fano threefolds and genus four curves
    Liu, Yuchen
    Zhao, Junyan
    JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2025,
  • [24] Rational points on log Fano threefolds over a finite field
    Gongyo, Yoshinori
    Nakamura, Yusuke
    Tanaka, Hiromu
    JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2019, 21 (12) : 3759 - 3795
  • [25] On the Picard number of almost Fano threefolds with pseudo-index >1
    Casagrande, Cinzia
    INTERNATIONAL JOURNAL OF MATHEMATICS, 2008, 19 (02) : 173 - 191
  • [26] Prime Fano threefolds of genus 12 with a G(m)-action and their automorphisms
    Kuznetsov, Alexander
    Prokhorov, Yuri
    EPIJOURNAL DE GEOMETRIE ALGEBRIQUE, 2018, 2
  • [27] Moduli spaces on the Kuznetsov component of Fano threefolds of index 2
    Department of Mathematics, University of Utah, Salt Lake City
    UT
    84102, United States
    不详
    G12 8QQ, United Kingdom
    arXiv, 2019,
  • [28] The Sp3-grassmannian and duality for prime Fano threefolds of genus 9
    Iliev, A
    MANUSCRIPTA MATHEMATICA, 2003, 112 (01) : 29 - 53
  • [29] The Sp3-grassmannian and duality for prime Fano threefolds of genus 9
    Atanas Iliev
    manuscripta mathematica, 2003, 112 : 29 - 53
  • [30] Very free rational curves in Fano varieties
    Coskun, Izzet
    Smith, Geoffrey
    JOURNAL OF ALGEBRA, 2022, 611 : 246 - 264
12345