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Yoshinori Gongyo

Publications and source records attributed to Yoshinori Gongyo.

At least 19 recordsLinked to original sources
arXiv2026

Non-vanishing of the structure-sheaf cohomology of affine henselian schemes and henselian affinoids

Let $(A,I)$ be a henselian pair such that $A$ is a domain of characteristic zero and $I\ne0$. We prove that any flat affine henselian scheme of finite presentation over $(A,I)$ has nonzero first structure-sheaf cohomology whenever one of its fibers over a point in $V(I)$ has positive dimension. This in particular gives a negative answer to the question by Devadas in the mixed-characteristic case. As an application, we also prove that the first structure-sheaf cohomology does not vanish for henselian affinoids of positive dimensions.

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arXiv2025

Characterization of products of projective spaces via nef complexity

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 complexity is non-negative and it is zero precisely for products of projective spaces. We classify smooth Fano threefolds with nef complexity at most one. In a similar vein, we prove Mukai's conjecture for smooth Fano varieties for which every extremal contraction is of fiber type and study smooth images of products of projective spaces. Along the way, we answer positively a question of J. Starr regarding the nef cone of smooth Fano varieties.

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arXiv2024

On generalized minimal log discrepancy

We discuss the ACC conjecture and the LSC conjecture for minimal log discrepancies of generalized pairs. We prove that some known results on these two conjectures for usual pairs are still valid for generalized pairs. We also discuss the theory of complements for generalized pairs.

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arXiv2023

Effective non-vanishing and Mukai type conjecture

We introduce some invariants of Fano varieties and propose a Mukai-type conjecture which characterizes the product of projective spaces. Moreover, we prove that the Ambro--Kawamata effective non-vanishing conjecture implies the Mukai-type conjecture.

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arXiv2023

Generalized complexity of surfaces

In this article, we introduce the generalized complexity of a generalized Calabi--Yau pair $(X,B,\textbf{M})$. This invariant compares the dimension of $X$ and Picard rank of $X$ with the sum of the coefficients of $B$ and $\textbf{M}$. It generalizes the complexity introduced by Shokurov. We show that a generalized log Calabi-Yau pair $(X,B,\textbf{M})$ of dimension $2$ with generalized complexity $0$ satisfies that $X$ is toric. This generalizes a result due to Brown, McKernan, Svaldi, and Zhong in the case of surfaces. Furthermore, we show that a generalized klt log Calabi-Yau surface $(X,\textbf{M})$ with generalized complexity $0$ satisfies that $X\simeq \mathbb{P}^2$ or $X\simeq \mathbb{P}^1\times \mathbb{P}^1$. Thus, this invariant interpolates between the characterization of toric varieties and the Kobayashi-Ochiai Theorem. As an application, we show that $3$-fold singularities with generalized complexity $0$ are toric. Furthermore, we show a local version of Kobayashi-Ochiai Theorem in dimension $3$.

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arXiv2018

Nef anti-canonical divisors and rationally connected fibrations

We study the Iitaka-Kodaira dimension of nef relative anti-canonical divisors. As a consequence, we prove that given a complex projective variety with klt singularities, if the anti-canonical divisor is nef, then the dimension of a general fibre of the maximal rationally connected fibration is at least the Iitaka-Kodaira dimension of the anti-canonical divisor.

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arXiv2016

Rational points on log Fano threefolds over a finite field

We prove the $W\mathcal{O}$-rationality of klt threefolds and the rational chain connectedness of klt Fano threefolds over a perfect field of characteristic $p>5$. As a consequence, any klt Fano threefold over a finite field has a rational point.

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arXiv2014

Versions of injectivity and extension theorems

We give an analytic version of the injectivity theorem by using multiplier ideal sheaves, and prove some extension theorems for the adjoint bundle of dlt pairs. Moreover, by combining techniques of the minimal model program, we obtain some results for semi-ampleness related to the abundance conjecture in birational geometry and the Strominger-Yau-Zaslow conjecture for hyperKähler manifolds.

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arXiv2014

Uniform bounds for strongly $F$-regular surfaces

We show that if $(X,B)$ is a two dimensional Kawamata log terminal pair defined over an algebraically closed field of characteristic $p$, and $p$ is sufficiently large, depending only on the coefficients of $B$, then $(X,B)$ is also strongly $F$-regular.

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arXiv2014

On the moduli b-divisors of lc-trivial fibrations

Roughly speaking, by using the semi-stable minimal model program, we prove that the moduli part of an lc-trivial fibration coincides with that of a klt-trivial fibration induced by adjunction after taking a suitable generically finite cover. As an application, we obtain that the moduli part of an lc-trivial fibration is b-nef and abundant by Ambro's result on klt-trivial fibrations.

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arXiv2013

On log canonical rings

We discuss the relationship among various conjectures in the minimal model theory including the finite generation conjecture of the log canonical rings and the abundance conjecture. In particular, we show that the finite generation conjecture of the log canonical rings for log canonical pairs can be reduced to that of the log canonical rings for purely log terminal pairs of log general type.

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