Blown-up Hirzebruch surfaces and special divisor classes

Jae Hyouk Lee, Yong Joo Shin

Research output: Contribution to journalArticlepeer-review

Abstract

We work on special divisor classes on blow-ups Fp,r of Hirzebruch surfaces over the field of complex numbers, and extend fundamental properties of special divisor classes on del Pezzo surfaces parallel to analogous ones on surfaces Fp,r. We also consider special divisor classes on surfaces Fp,r with respect to monoidal transformations and explain the tie-ups among them contrast to the special divisor classes on del Pezzo surfaces. In particular, the fundamental properties of quartic rational divisor classes on surfaces Fp,r are studied, and we obtain interwinded relationships among rulings, exceptional systems and quartic rational divisor classes along with monoidal transformations. We also obtain the effectiveness for the rational divisor classes on Fp,r with positivity condition.

Original languageEnglish
Article number867
JournalMathematics
Volume8
Issue number6
DOIs
StatePublished - 1 Jun 2020

Bibliographical note

Funding Information:
Funding: The first author was supported supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. 2019R1F1A1058962). The second author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education(No. 2017R1D1A1B03028273) and by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education: NRF-2018R1D1A1B07048385.

Publisher Copyright:
© 2020 by the authors.

Keywords

  • Hirzebruch surface
  • Monoidal transformation
  • Special divisor

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