The Irreducibility of the Spaces of Rational Curves on del Pezzo Manifolds-Reference-Cited by-同舟云学术

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The Irreducibility of the Spaces of Rational Curves on del Pezzo Manifolds

Published:2024-04-26 Issue:12 Volume:2024 Page:9893-9909
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Okamura Fumiya¹

Affiliation:

1. Graduate School of Mathematics, Nagoya University , Furo-cho, Chikusa-ku, Nagoya, 464-8601, Japan

Abstract

Abstract We prove the irreducibility of the spaces of rational curves on del Pezzo manifolds of Picard rank $1$ and dimension $n \ge 4$ by analyzing the fibers of evaluation maps. As a corollary, we prove Geometric Manin’s Conjecture in these cases.

Publisher

Oxford University Press (OUP)

Link

https://academic.oup.com/imrn/article-pdf/2024/12/9893/58270838/rnae080.pdf

Reference41 articles.

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3. Tamagawa numbers of polarized algebraic varieties;Batyrev;Nombre et répartition de points de hauteur bornée (Paris, 1996),1998

4. Spaces of rational curves on complete intersections;Beheshti;Compos. Math.,2013

5. Moduli spaces of rational curves on Fano threefolds;Beheshti;Adv. Math,2022

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