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J. Korean Math. Soc. 2023; 60(2): 359-374

Online first article February 16, 2023      Printed March 1, 2023

https://doi.org/10.4134/JKMS.j220101

Copyright © The Korean Mathematical Society.

The Harbourne-Hirschowitz condition and the anticanonical orthogonal property for surfaces

Abel Castorena, Juan Bosco Fr\'ias-Medina

Antigua Carretera a P\'atzcuaro 8701, Col. Ex-Hacienda San Jos\'e de la Huerta; Avenida Francisco J. M\'ugica s/n, Colonia Felicitas del R\'io

Abstract

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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: Regular surfaces, Kodaira dimension, anticanonical class

MSC numbers: Primary 14C20, 14J26, 14J28; Secondary 14J27, 14J29

Supported by: The first author is supported by Grants PAPIIT UNAM IN100419 ``Aspectos Geom\'etricos del moduli de curvas $M_g$" and CONACyT, M\'exico A1-S-9029 ``Moduli de curvas y curvatura en $A_g$". The second author acknowledges the support of Programa de Becas Posdoctorales 2019, DGAPA, UNAM during 2021. The second author was supported by ``Programa de Estancias Posdoctorales por M\'exico Convocatoria 2021 de CONACYT" during the revisions of this paper.

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