Kiwamu Watanabe

activity

20232025

collaborators

6 papers

math.AG2025

Characterization of products of projective spaces via nef complexity

Joshua Enwright, Stefano Filipazzi, Yoshinori Gongyo +4

We define the nef complexity of a projective variety $X$ . This invariant compares $dim X + ρ (X)$ with the sum of the coefficients of nef partitions of $- K_{X}$ . We prove that the nef…

math.AG2024

Smooth Fano varieties with pseudoindex equal to half of their dimension

Kiwamu Watanabe

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 $X$ w…

math.AG2024

Quadratic Varieties of Small Codimension

Kiwamu Watanabe

Let $X \subset P^{n + c}$ be a nondegenerate smooth projective variety of dimension $n$ defined by quadratic equations. For such varieties, P. Ionescu and F. Russo proved th…

math.AG2024

Fano varieties of middle pseudoindex

Kiwamu Watanabe

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 $\frac{dim X + 1}{2}$ and the Picard…

math.AG2024

Classification of smooth Fano varieties with large pseudoindex

Kiwamu Watanabe

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 o…

math.AG2023

Fano varieties with large pseudoindex and non-free rational curves

Kiwamu Watanabe

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…