Classifying sections of del Pezzo fibrations, I

被引：3
作者：
Lehmann, Brian [1 ]
Tanimoto, Sho [2 ,3 ]
机构：
[1] Boston Coll, Dept Math, Chestnut Hill, MA 02467 USA
[2] Nagoya Univ, Grad Sch Math, Nagoya 4648602, Japan
[3] Nagoya Univ, Inst Adv Res, Nagoya 4648602, Japan
来源：
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | 2024年 / 26卷 / 01期
关键词：
Moduli space of sections; Fano variety; rational curves; Manin's conjecture; RATIONAL CURVES; WEAK APPROXIMATION; MANINS CONJECTURE; FUNCTION-FIELDS; BOUNDED HEIGHT; FAMILIES; BUNDLES; SPACES; HYPERSURFACES; VARIETIES;
D O I：
10.4171/JEMS/1363
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We develop a strategy to classify the components of the space of sections of a del Pezzo fibration over P1. In particular, we prove the Movable Bend -and -Break lemma for del Pezzo fibrations. Our approach is motivated by Geometric Manin's Conjecture and proves upper bounds on the associated counting function. We also give applications to enumerativity of Gromov-Witten invariants and to the study of the Abel-Jacobi map.
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页码：289 / 354
页数：66
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