Masatomo Sawahara

activity

20192026

most citedCylinders in weak del Pezzo fibrations

4 citations · 11 across the 12 of their papers we have counts for

collaborators

12 papers

math.AG2026

Flexibility of affine cones over blow-ups of weighted projective planes

In-Kyun Kim, Dae-Won Lee, Masatomo Sawahara

Let $S_{m}^{n}$ be the surface obtained by blowing up $P (1, 1, m)$ at $n$ general smooth points, where $m \geq 2$ . For every very ample Cartier divisor $H$ on $S_{m}^{n}$ , we prove th…

math.AG2026

Polarized cylinders on blow-ups of weighted projective planes

In-Kyun Kim, Masatomo Sawahara, Joonyeong Won

We study polarized cylinders in certain rational surfaces arising from blow-ups of weighted projective planes. In particular, we consider the surfaces obtained by blowing up $m + 4$ …

math.AG2025

Cylindricity of weighted singular del Pezzo surfaces over fields of characteristic zero

In-Kyun Kim, Dae-Won Lee, Masatomo Sawahara

In this paper, we study the cylindricity of $k$ -forms of singular del Pezzo surfaces obtained by blowing up weighted projective planes $P (1, 1, m)$ over an arbitrary fie…

math.AG2025

Cylinders in Du Val del Pezzo surfaces of degree one with Picard rank two

Jaehyun Kim, Dae-Won Lee, Masatomo Sawahara

We prove that for Du Val del Pezzo surfaces of degree one with Picard rank two, the existence of an anticanonical polar cylinder implies the ample polar cylindricity.

math.AG2024

Polarized cylinders in Du Val del Pezzo surfaces of degree two

Masatomo Sawahara

Let $S$ be a del Pezzo surface with at worst Du Val singularities of degree $2$ such that $S$ admits an $(- K_{S})$ -polar cylinder. In this article, we construct an $H$ -polar cylinder…

math.AG2024

Minimal compactifications of the affine plane with only star-shaped singularities

Masatomo Sawahara

We consider minimal compactifications of the complex affine plane. Minimal compactifications of the affine plane with at most log canonical singularities are classified. Moreover,…

math.AG2023★ 1 cited

Minimal compactifications of the affine plane with nef canonical divisors

Masatomo Sawahara

We shall consider minimal analytic compactifications of the affine plane with singularities. In previous work, Kojima and Takahashi proved that any minimal analytic compactificatio…

math.AG2023

Cylindrical ample divisors on Du Val del Pezzo surfaces

Masatomo Sawahara

Let $S$ be a del Pezzo surface with at worse Du Val singularities of degree $\geq 3$ . We construct an $H$ -polar cylinder for any ample $Q$ -divisor $H$ on $S$ .

math.AG2022

Notes on cylinders in smooth projective surfaces

Masatomo Sawahara

In this article, we determine the existing condition of cylinders in smooth minimal geometrically rational surfaces over a perfect field. Furthermore, we show that for any biration…

math.AG2021★ 3 cited

Compactifications of the affine plane over non-closed fields

Masatomo Sawahara

In this article, we give the classification of normal del Pezzo surfaces of rank one with at most log canonical singularities containing the affine plane defined over an algebraica…

math.AG2020★ 3 cited

Cylinders in canonical del Pezzo fibrations

Masatomo Sawahara

Cylinders in projective varieties play an important role in connection with unipotent group actions on certain affine algebraic varieties. The previous work due to Dubouloz and Kis…

math.AG2019★ 4 cited

Cylinders in weak del Pezzo fibrations

Masatomo Sawahara

In this article, we shall look into the existence of vertical cylinders contained in a weak del Pezzo fibration as a generalization of the former work due to Dubouloz and Kishimoto…