arXiv subjects

Hirotaka Onuki

Publications and source records attributed to Hirotaka Onuki.

4 recordsLinked to original sources

arXiv2026

On the effective generation of direct images of pluricanonical bundles in mixed characteristic

We present an effective global generation result for direct images of pluricanonical bundles in mixed characteristic. This is a mixed characteristic analog of Ejiri's theorem in positive characteristic and the theorem of Popa and Schnell regarding their Fujita-type conjecture in characteristic zero. As an application, we establish a weak positivity statement for the relative canonical sheaf of a smooth morphism in mixed characteristic.

math.AG↗

arXiv2026

Global $+$-regularity of regular del Pezzo surfaces in mixed characteristic

Let $R = W(k)$ be the ring of Witt vectors over an algebraically closed field $k$ of characteristic $p > 2$. Let $M$ be a three-dimensional regular integral flat projective $R$-scheme such that $H^0(M,\mathcal{O}_M) = R$ and the anticanonical sheaf $ω_M^{-1}$ is ample. We show that $M$ is globally $+$-regular if the closed fiber $M_k$ is reduced.

math.AG↗

arXiv2025

Quasi-$F$-splitting and smooth weak del Pezzo surfaces in mixed characteristic

We introduce the notion of quasi-$F$-splitting in mixed characteristic and study Kodaira-type vanishing on quasi-$F$-splitting varieties. As an application, we prove a Kodaira-type vanishing on lifts of rational double point (RDP) del Pezzo surfaces.

math.AG↗

arXiv2024

On the Complexity of Interpolation by Polynomials with Non-negative Real Coefficients

In this paper, we consider interpolation by \textit{completely monotonous} polynomials (CMPs for short), that is, polynomials with non-negative real coefficients. In particular, given a finite set $S\subset \mathbb{R}_{>0} \times \mathbb{R}_{\geq 0}$, we consider \textit{the minimal polynomial} of $S$, introduced by Berg [1985], which is `minimal,' in the sense that it is eventually majorized by all the other CMPs interpolating $S$. We give an upper bound of the degree of the minimal polynomial of $S$ when it exists. Furthermore, we give another algorithm for computing the minimal polynomial of given $S$ which utilizes an order structure on sign sequences. Applying the upper bound above, we also analyze the computational complexity of algorithms for computing minimal polynomials including ours.

math.NA↗