arXiv subjects

Takeru Fukuoka

Publications and source records attributed to Takeru Fukuoka.

6 recordsLinked to original sources

arXiv2025

Rank two weak Fano bundles on del Pezzo threefolds of degree five

This paper classifies rank two vector bundles on a del Pezzo threefold $X$ of degree five whose projectivizations are weak Fano. This classification is then used to determine properties of the moduli spaces of such vector bundles on $X$, and we determine precisely when the moduli spaces are smooth, irreducible, and fine. We also prove that such a bundle on a del Pezzo threefold of degree one or two splits, and as result give a classification of weak Fano bundles of rank two on a del Pezzo threefold of Picard rank one.

math.AG↗

arXiv2025

Rank two Weak Fano bundles on Fano threefolds of Picard rank one

We classify rank two vector bundles on a Fano threefold of Picard rank one whose projectivizations are weak Fano. We also prove the existence of examples for each case of the classification result. Our classification includes detailed resolutions of them on the quadric threefold.

math.AG↗

arXiv2022

Classification of rank two weak Fano bundles on del Pezzo threefolds of degree four

We classify rank two vector bundles on a given del Pezzo threefold of degree four whose projectivizations are weak Fano into seven cases. We also give an example for each of these seven cases.

math.AG↗

arXiv2019

Refinement of the classification of weak Fano threefolds with sextic del Pezzo fibrations

We refine the classification of weak Fano threefolds with sextic del Pezzo fibrations by considering the Hodge numbers of them. By the refined classification result, such threefolds are classified into 17 cases. The main result of this paper is to show that there exists an example for each of 17 cases, except for 2 cases.

math.AG↗

arXiv2018

Relative linear extensions of sextic del Pezzo fibrations

In this paper, we study a sextic del Pezzo fibration over a curve comprehensively. We obtain certain formulae of several basic invariants of such a fibration. We also establish the embedding theorem of such a fibration which asserts that every such a fibration is a relative linear section of a Mori fiber space with the general fiber $(\mathbb{P}^{1})^{3}$ and that with the general fiber $(\mathbb{P}^{2})^{2}$. As an application of this embedding theorem, we classify singular fibers of such a fibrations and answer a question of T. Fujita about existence of non-normal fibers.

math.AG↗

arXiv2016

On the existence of almost Fano threefolds with del Pezzo fibrations

By Jahnke-Peternell-Radloff and Takeuchi, almost Fano threefolds with del Pezzo fibrations were classified. Among them, there exists 10 classes such that the existence of members of these was not proved. In this paper, we construct such examples belonging to each of 10 classes.

math.AG↗