紀要論文

紀要論文

text

Osaka Journal of Mathematics. 2025, 62(1), p. 19-50

NON-FREE CURVES ON FANO VARIETIES

Osaka University and Osaka City University, Departments of Mathematics

英語

text

2025-01

Let X be a smooth Fano variety over ℂ and let B be a smooth projective curve over ℂ. Geometric Manin's Conjecture predicts the structure of the irreducible components M ⊂ Mor(B, X) parametrizing curves which are non-free and have large anticanonical degree. Following ideas of [19], we prove the first prediction of Geometric Manin's Conjecture describing such irreducible components. As an application, we prove that there is a proper closed subset V ⊂ X such that all non-dominant components of Mor(B, X) parametrize curves in V, verifying an expectation put forward by Victor Batyrev. We also demonstrate two important ways that studying Mor(B, X) differs from studying the space of sections of a Fano fibration X → B.

10.18910/100443

100443

NON-FREE CURVES ON FANO VARIETIES

Osaka University and Osaka City University, Departments of Mathematics

英語

2025-01

Osaka Journal of Mathematics

62

1

19

50

https://hdl.handle.net/11094/100443

10.18910/100443

https://doi.org/10.18910/100443