arXiv subjects

Yuto Masamura

Publications and source records attributed to Yuto Masamura.

4 recordsLinked to original sources

arXiv2026

Relative cone of curves and extremal contractions of a successive blowup

Let $X$ be a normal variety, and let $π\colon\tilde X\to X$ be the successive blowup along subvarieties $Z_1,\dotsc,Z_n\subseteq X$ of codimension at least two that have simple normal crossings and satisfy $Z_h\not\supseteq Z_i$ whenever $h<I$. We prove that the relative cone of curves $\overline{\operatorname{NE}}(\tilde X/X)$ is generated by the classes of finitely many elementary curves, and that every face admits a contraction over $X$. We describe the exceptional loci of extremal ray contractions, and prove that every small extremal ray contraction admits a $D$-flip for every $\mathbb R$-Cartier divisor $D$ negative on the corresponding ray.

math.AG↗

arXiv2026

A construction of smooth varieties admitting small contractions

Given a smooth variety together with two smooth subvarieties, we construct, via two successive blowups, smooth varieties admitting small contractions. This generalizes Kawamata's example of small contraction in dimension 4. We also construct the flip of the contraction explicitly. As an application, from products of two del Pezzo surfaces we obtain smooth weak Fano fourfolds that admit small contractions with Picard number up to 10.

math.AG↗

arXiv2025

Relations between indices of Calabi--Yau varieties and pairs

We show that for any smooth Calabi--Yau variety, its index can be realized as the index of a Kawamata log terminal (klt) Calabi--Yau pair of lower dimension with standard coefficients. Our approach is based on an inductive argument on the dimension using the Beauville--Bogomolov decomposition. A key step in the argument is to prove that for $n\ge3$, any positive integer $m$ satisfying $φ(m)\le 2n$ can be realized as the index of a klt Calabi--Yau pair of dimension $n-1$.

math.AG↗

arXiv2023

On boundedness of indices of minimal pairs -- surfaces

For given positive integers $d$ and $m$, consider the projective klt pairs $(X,B)$ of dimension $d$, of Cartier index $m$, and with semi-ample $K_X+B$ defining a contraction $π\colon X\to Z$. We prove that it is not possible in general to write $n(K_X+B)\simπ^*A_Z$ for some $n$ depending only on $d$ and $m$, and some Cartier divisor $A_Z$ on $Z$.

math.AG↗