Classifying sections of del Pezzo fibrations, I

Brian Lehmann; Sho Tanimoto

Classifying sections of del Pezzo fibrations, I

Algebraic Geometry 2022-11-03 v3

Authors: Brian Lehmann , Sho Tanimoto

Abstract

We develop a strategy to classify the components of the space of sections of a del Pezzo fibration over $\mathbb{P}^{1}$ . 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.

Keywords

del Pezzo fibration space of sections movable bend and break geometric Manin conjecture counting function Gromov-Witten invariant Abel-Jacobi map

Cite

@article{arxiv.1912.04369,
  title  = {Classifying sections of del Pezzo fibrations, I},
  author = {Brian Lehmann and Sho Tanimoto},
  journal= {arXiv preprint arXiv:1912.04369},
  year   = {2022}
}

Comments

Minor changes, 59 pages, to appear in Journal of the European Mathematical Society,

Classifying sections of del Pezzo fibrations, I

Abstract

Keywords

Cite

Comments

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