arXiv subjects

Kiwamu Watanabe

Publications and source records attributed to Kiwamu Watanabe.

25 records · Page 2Linked to original sources

arXiv2014

Rational curves, Dynkin diagrams and Fano manifolds with nef tangent bundle

A Fano manifold $X$ with nef tangent bundle is of flag-type if it has the same type of elementary contractions as a complete flag manifold. In this paper we present a method to associate a Dynkin diagram $\mathcal{D}(X)$ with any such $X$, based on the numerical properties of its contractions. We then show that $\mathcal{D}(X)$ is the Dynkin diagram of a semisimple Lie group. As an application we prove that Campana-Peternell conjecture holds when $X$ is a flag-type manifold whose Dynkin diagram is $A_n$ ($X$ is shown to be the complete flag in $\mathbb{P}^n$).

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arXiv2013

Fano 5-folds with nef tangent bundles and Picard numbers greater than one

We prove that smooth Fano 5-folds with nef tangent bundles and Picard numbers greater than one are rational homogeneous manifolds.

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arXiv2013

P1-bundles over projective manifolds of Picard number one each of which admit another smooth morphism of relative dimension one

We give a complete classification of P1-bundles over a projective manifold of Picard number one which admit another smooth morphism of relative dimension one.

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arXiv2011

On projective manifolds swept out by cubic varieties

We study structures of embedded projective manifolds swept out by cubic varieties. We show if an embedded projective manifold is swept out by high-dimensional smooth cubic hypersurfaces, then it admits an extremal contraction which is a linear projective bundle or a cubic fibration. As an application, we give a characterization of smooth cubic hypersurfaces. We also classify embedded projective manifolds of dimension at most five swept out by copies of the Segre threefold P^1\timesP^2. In the course of the proof, we classify projective manifolds of dimension five swept out by planes.

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arXiv2011

A bound of lengths of chains of minimal rational curves on Fano manifolds of Picard number 1

In this paper, we investigate the minimal length of chains of minimal rational curves needed to join two general points on a Fano manifold of Picard number 1. In particular, we give a sharp bound of the length by a fundamental argument. As an application, we compute the length for Fano manifolds of dimension < 8.

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arXiv2011

Classification of embedded projective manifolds swept out by rational homogeneous varieties of codimension one

We give a classification of embedded smooth projective varieties swept out by rational homogeneous varieties whose Picard number and codimension are one.

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arXiv2010

Lengths of chains of minimal rational curves on Fano manifolds

In this paper, we consider a natural question how many minimal rational curves are needed to join two general points on a Fano manifold X of Picard number 1. In particular, we study the minimal length of such chains in the cases where the dimension of X is at most 5, the coindex of X is at most 3 and X equips with a structure of a double cover. As an application, we give a better bound on the degree of Fano 5-folds of Picard number 1.

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