Work

Bigness of the Tangent Bundle of a Fano Threefold With Picard Number Two

Year: 2024

Type: article

Abstract: In this paper, we study the positivity property of the tangent bundle $T_X$ of a Fano threefold X with Picard number $2$ . We determine the bigness of the tangent bundle of the whole $36$ deformation types. Our result shows that $T_X$ is big if and only if $(-K_X)^3\ge 34$ . As a corollary, we prove that the tangent bundle is not big when X has a standard conic bundle structure with non-empty discriminant. Our main methods are to produce irreducible effective divisors on ${\mathbb {P}}(T_X)$ constructed from the total dual VMRT associated to a family of rational curves. Additionally, we present some criteria to determine the bigness of $T_X$ .

Source: Nagoya Mathematical Journal

DOI: 10.1017/nmj.2024.24

Authors: HOSUNG KIM, JEONG-SEOP KIM, YONGNAM LEE

Institutions: Changwon National University, Korea Institute for Advanced Study, Korea Advanced Institute of Science and Technology, Institute for Basic Science

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: Institute for Basic Science, Ministry of Science and ICT, South Korea

Award: G2894305487