Zobrazeno 1 - 10
of 139
pro vyhledávání: '"Watanabe, Kiwamu"'
Autor:
Watanabe, Kiwamu
Let $X$ be a complex smooth Fano variety of dimension $n$. Assume that $X$ admits a birational contraction of an extremal ray. In this paper, we give a classification of such $X$ when the pseudoindex is equal to $\frac{\dim X}{2}$.
Comment: 14 p
Comment: 14 p
Externí odkaz:
http://arxiv.org/abs/2411.00379
Autor:
Watanabe, Kiwamu
Let $X \subset \mathbb P^{n+c}$ be a nondegenerate smooth projective variety of dimension $n$ defined by quadratic equations. For such varieties, P. Ionescu and F. Russo proved the Hartshorne conjecture on complete intersections, which states that X
Externí odkaz:
http://arxiv.org/abs/2405.04002
Autor:
Watanabe, Kiwamu
Let $X$ be a complex smooth Fano variety of dimension $n$. In this paper, we give a classification of such $X$ when the pseudoindex is equal to $\dfrac{\dim X+1}{2}$ and the Picard number greater than one.
Comment: 7 pages, to appear in Manuscri
Comment: 7 pages, to appear in Manuscri
Externí odkaz:
http://arxiv.org/abs/2403.14065
Autor:
Watanabe, Kiwamu
Let $X$ be a complex smooth Fano variety of dimension at least four. In this paper, we classify such $X$ when the pseudoindex is at least $n-2$ and the Picard number greater than one. We also discuss the relations between pseudoindex and other invari
Externí odkaz:
http://arxiv.org/abs/2402.14283
Autor:
Watanabe, Kiwamu
For $n\geq 4$, let $X$ be a complex smooth Fano $n$-fold whose minimal anticanonical degree of non-free rational curves on $X$ is at least $n-2$. We classify extremal contractions of such varieties. As an application, we obtain a classification of Fa
Externí odkaz:
http://arxiv.org/abs/2309.03438
Autor:
Takahashi, Yuta, Watanabe, Kiwamu
In characteristic $0$, the Campana-Peternell conjecture claims that the only smooth Fano variety with nef tangent bundle should be homogeneous. In this paper, we study the positive characteristic version of the Campana-Peternell conjecture. In partic
Externí odkaz:
http://arxiv.org/abs/2210.17055
Autor:
Watanabe, Kiwamu
Let $X$ be a complex smooth projective variety such that the exterior power of the tangent bundle $\bigwedge^{r} T_X$ is nef for some $1\leq r<\dim X$. We prove that, up to an \'etale cover, $X$ is a Fano fiber space over an Abelian variety. This giv
Externí odkaz:
http://arxiv.org/abs/2208.06735
Autor:
Kanemitsu, Akihiro, Watanabe, Kiwamu
Let $X$ be a smooth projective variety defined over an algebraically closed field of positive characteristic $p$ whose tangent bundle is nef. We prove that $X$ admits a smooth morphism $X \to M$ such that the fibers are Fano varieties with nef tangen
Externí odkaz:
http://arxiv.org/abs/2012.09419
Autor:
Watanabe, Kiwamu
Let $X$ be a smooth complex projective variety with nef $\bigwedge^2 T_X$ and $\dim X \geq 3$. We prove that, up to a finite \'etale cover $\tilde{X} \to X$, the Albanese map $\tilde{X} \to {\rm Alb}(\tilde{X})$ is a locally trivial fibration whose f
Externí odkaz:
http://arxiv.org/abs/2011.01427
Autor:
Watanabe, Kiwamu
We prove that any Fano manifold of coindex three admitting nef tangent bundle is homogeneous.
Comment: 14 pages
Comment: 14 pages
Externí odkaz:
http://arxiv.org/abs/1904.10185