Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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THE HARBOURNE-HIRSCHOWITZ CONDITION AND THE ANTICANONICAL ORTHOGONAL PROPERTY FOR SURFACES

  • Abel Castorena (Centro de Ciencias Matematicas Universidad Nacional Autonoma de Mexico, Campus Morelia) ;
  • Juan Bosco Frias-Medina (Instituto de Fisica y Matematicas Universidad Michoacana de San Nicolas de Hidalgo Edificio C-3, Ciudad Universitaria)
  • Received : 2022.03.03
  • Accepted : 2022.12.12
  • Published : 2023.03.01
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Abstract

In this paper we give the first steps toward the study of the Harbourne-Hirschowitz condition and the anticanonical orthogonal property for regular surfaces. To do so, we consider the Kodaira dimension of the surfaces and study the cases based on the Enriques-Kodaira classification.

Keywords

Acknowledgement

We would like to thank Mustapha Lahyane for his comments to improve this work. Also, we thank the anonymous referees for their suggestions and remarks to improve the quality of this paper.

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