Takuzo Okada

activity

20112026

most citedBirational Mori fiber structures of Q-Fano 3-fold weighted complete intersections, II

27 citations · 122 across the 27 of their papers we have counts for

collaborators

28 papers

math.AG2026

K-stability and birational rigidity of Fano 3-fold weighted complete intersections

Takuzo Okada

We show that any birationally rigid well-formed and quasismooth Fano 3-fold weighted complete intersection is K-stable.

math.AG2026

Local inequalities for $cD$ and $c E$ singularities

Chi-Kang Chang, Jheng-Jie Chen, Takuzo Okada

We obtain inequalities for isolated $c D_{n}, c E_{6}, c E_{7}$ and $c E_{8}$ singularities, analogues of the $4 μ^{2} / (n + 1)$ -inequality for isolated $c A_{n}$ singularity in \cite{KOP}. These inequ…

math.AG2025

Local inequalities for $c A_{k}$ singularities

Igor Krylov, Takuzo Okada, Erik Paemurru

We generalize an intersection-theoretic local inequality of Fulton-Lazarsfeld to weighted blowups. As a consequence, we obtain the $4 n^{2} / (k + 1)$ -inequality for isolated $c A_{k}$ singu…

math.AG2025

A survey on birational Rigidity of threefold Weighted Complete Intersections

Tiago Duarte Guerreiro, Takuzo Okada

We survey what is known about Fano threefold weighted complete intersections from the point of view of birational rigidity.

math.AG2025

Birational geometry of weighted complete intersections of type $(12, 14)$ in $P (1, 2, 3, 4, 7, 11)$

Takuzo Okada

We show that any quasismooth Fano threefold weighted complete intersections of type $(12, 14)$ in $P (1, 2, 3, 4, 7, 11)$ is birationally solid.

math.AG2024

K-stablity of Fano threefold hypersurfaces of index 1

Livia Campo, Takuzo Okada

We settle the problem of K-stability of quasi-smooth Fano 3-fold hypersurfaces with Fano index 1 by providing lower bounds for their delta invariants. We use the method introduced…

math.AG2023

Birationally solid Fano 3-fold hypersurfaces

Takuzo Okada

A Fano variety of Picard number $1$ is said to be \textit{birationally solid} if it is not birational to a Mori fiber space over a positive dimensional base. In this paper we compl…

math.AG2022

K-stable divisors in $P^{1} \times P^{1} \times P^{2}$ of degree $(1, 1, 2)$

Ivan Cheltsov, Kento Fujita, Takashi Kishimoto +1

We prove that every smooth divisor in $P^{1} \times P^{1} \times P^{2}$ of degree $(1, 1, 2)$ is K-stable.

math.AG2022★ 3 cited

$2 n^{2}$ -inequality for $c A_{1}$ points and applications to birational rigidity

Igor Krylov, Takuzo Okada, Erik Paemurru +1

The $4 n^{2}$ -inequality for smooth points plays an important role in the proofs of birational (super)rigidity. The main aim of this paper is to generalize such an inequality to term…

math.AG2020★ 2 cited

K-stability of birationally superrigid Fano 3-fold weighted hypersurfaces

In-Kyun Kim, Takuzo Okada, Joonyeong Won

We prove that the alpha invariant of a quasi-smooth Fano 3-fold weighted hypersurface of index $1$ is greater than or equal to $1/2$ . Combining this with the result of Stibitz and…

math.AG2019★ 1 cited

Alpha invariants of birationally bi-rigid Fano 3-folds I

In-Kyun Kim, Takuzo Okada, Joonyeong Won

We compute global log canonical thresholds of certain birationally bi-rigid Fano 3-folds embedded in weighted projective spaces as complete intersections of codimension 2 and prove…

math.AG2019★ 4 cited

Birationally superrigid Fano 3-folds of codimension 4

Takuzo Okada

We determine birational superrigidity for a quasi-smooth prime Fano 3-fold of codimension 4 with no projection centers. In particular we prove birational superrigidity for Fano 3-f…

math.AG2018★ 4 cited

On birational rigidity of singular del Pezzo fibrations of degree 1

Takuzo Okada

We give a sufficient condition for birational superrigidity of del Pezzo fibrations of degree $1$ with only $\frac{1}{2} (1, 1, 1)$ singular points, generalizing the so called $K^{2}$ -…

math.AG2017★ 1 cited

Smooth weighted hypersurfaces that are not stably rational

Takuzo Okada

We prove the failure of stable rationality for many smooth well formed weighted hypersurfaces of dimension at least 3. It is in particular proved that a very general smooth well fo…

math.AG2017★ 1 cited

Stable rationality of index one Fano hypersurfaces containing a linear space

Takuzo Okada

We prove that a very general complex hypersurface of degree $n + 1$ in $P^{n + 1}$ containing an $r$ -plane with multiplicity $m$ is not stably rational for $n \geq 3$ , $m, r >…

math.AG2017★ 8 cited

Stable rationality of del Pezzo fibrations of low degree over projective spaces

Igor Krylov, Takuzo Okada

The main aim of this article is to show that a very general 3-dimensional del Pezzo fibration of degree 1,2,3 is not stably rational except for a del Pezzo fibration of degree 3 be…

math.AG2016★ 18 cited

Stable rationality of higher dimensional conic bundles

Hamid Abban, Takuzo Okada

We prove that a very general nonsingular conic bundle $X \to P^{n - 1}$ embedded in a projective vector bundle of rank $3$ over $P^{n - 1}$ is not stably ration…

math.AG2016★ 6 cited

Stable rationality of orbifold Fano threefold hypersurfaces

Takuzo Okada

We determine the rationality of very general quasismooth Fano 3-fold weighted hypersurfaces completely and determine the stable rationality of them except for cubic 3-folds. More p…

math.AG2016★ 22 cited

Stable rationality of cyclic covers of projective spaces

Takuzo Okada

The main aim of this paper is to show that a cyclic cover of $P^{n}$ branched along a very general divisor of degree $d$ is not stably rational provided that $n \geq 3$ and $…

math.AG2016★ 3 cited

Alpha invariants of birationally rigid Fano threefolds

In-Kyun Kim, Takuzo Okada, Joonyeong Won

We compute global log canonical thresholds, or equivalently alpha invariants, of birationally rigid orbifold Fano threefolds embedded in weighted projective spaces as codimension t…

math.AG2015

Birationally rigid Pfaffian Fano 3-folds

Hamid Abban, Takuzo Okada

We classify birationally rigid orbifold Fano 3-folds of index one defined by $5 \times 5$ Pfaffians. We give a sharp criterion for birational rigidity of these families based on th…

math.AG2015

Nonrational del Pezzo fibrations admitting an action of the Klein simple group

Takuzo Okada

We present a series of del Pezzo fibrations of degree $2$ admitting an action of the Klein simple group and prove their nonrationality by the reduction modulo $p$ method of Kollár.…

math.AG2015

Birational rigidity of del Pezzo fibrations with quotient singularities and its application

Takuzo Okada

In this paper we give a criterion for birational rigidity of del Pezzo fibrations of degree 1 and 2 with only quotient singularities. As an application, we prove birational rigidit…

math.AG2014★ 14 cited

Birational Mori fiber structures of $Q$ -Fano $3$ -fold weighted complete intersections, III

Takuzo Okada

This is a continuation of a series of papers studying the birational Mori fiber structures of anticanonically embedded $Q$ -Fano $3$ -fold weighted complete intersections of…

K-stability and birational rigidity of Fano 3-fold weighted complete intersections

Local inequalities for cD and cE singularities

Local inequalities for cAk​ singularities

A survey on birational Rigidity of threefold Weighted Complete Intersections

Birational geometry of weighted complete intersections of type (12,14) in P(1,2,3,4,7,11)

K-stablity of Fano threefold hypersurfaces of index 1

Birationally solid Fano 3-fold hypersurfaces

K-stable divisors in P1×P1×P2 of degree (1,1,2)

2n2-inequality for cA1​ points and applications to birational rigidity

K-stability of birationally superrigid Fano 3-fold weighted hypersurfaces

Alpha invariants of birationally bi-rigid Fano 3-folds I

Birationally superrigid Fano 3-folds of codimension 4

On birational rigidity of singular del Pezzo fibrations of degree 1

Smooth weighted hypersurfaces that are not stably rational

Stable rationality of index one Fano hypersurfaces containing a linear space

Stable rationality of del Pezzo fibrations of low degree over projective spaces

Stable rationality of higher dimensional conic bundles

Stable rationality of orbifold Fano threefold hypersurfaces

Stable rationality of cyclic covers of projective spaces

Alpha invariants of birationally rigid Fano threefolds

Birationally rigid Pfaffian Fano 3-folds

Nonrational del Pezzo fibrations admitting an action of the Klein simple group

Birational rigidity of del Pezzo fibrations with quotient singularities and its application

Birational Mori fiber structures of Q-Fano 3-fold weighted complete intersections, III

Local inequalities for $cD$ and $c E$ singularities

Local inequalities for $c A_{k}$ singularities

Birational geometry of weighted complete intersections of type $(12, 14)$ in $P (1, 2, 3, 4, 7, 11)$

K-stable divisors in $P^{1} \times P^{1} \times P^{2}$ of degree $(1, 1, 2)$

$2 n^{2}$ -inequality for $c A_{1}$ points and applications to birational rigidity

Birational Mori fiber structures of $Q$ -Fano $3$ -fold weighted complete intersections, III