Cylindrical ample divisors on Du Val del Pezzo surfaces

Masatomo Sawahara

doi:10.1515/forum-2024-0279

Article

Cylindrical ample divisors on Du Val del Pezzo surfaces

Masatomo Sawahara

Published/Copyright: January 13, 2025

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From the journal Forum Mathematicum Volume 37 Issue 5

Abstract

The existence of polarized cylinders in normal projective varieties corresponds to admitting non-trivial 𝔾 a -action on their affine cones defined by the polarized pairs. Note that a criterion for polarized cylinders in smooth del Pezzo surfaces is studied. Hence, we observe the existing condition of polarized cylinders in del Pezzo surfaces with at worst Du Val singularities. Let S be a del Pezzo surface with at worst Du Val singularities of degree ≥ 3 . We then construct an H-polar cylinder for any ample ℚ -divisor H on S.

Keywords: Polarized cylinder; rational surface; Du Val singularity

MSC 2020: 14C20; 14E05; 14J17; 14J26; 14J45; 14R25

Communicated by Jan Bruinier

Funding statement: The author was supported by the Foundation of Research Fellows, The Mathematical Society of Japan.

Acknowledgements

The author would like to thank the referees for useful comments that helped to improve this article.

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Received: 2024-06-17

Revised: 2024-10-16

Published Online: 2025-01-13

Published in Print: 2025-06-01

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Articles in the same Issue

https://doi.org/10.1515/forum-2024-0279

Keywords for this article

Polarized cylinder; rational surface; Du Val singularity