The Harbourne-Hirschowitz condition and the Anticanonical Orthogonal Property for surfaces
Abel Castorena, Juan Bosco Fr\'ias-Medina
TL;DR
This paper explores the Harbourne-Hirschowitz condition and the Anticanonical Orthogonal Property for regular surfaces, analyzing their behavior across different surface classifications based on Kodaira dimension.
Contribution
It initiates the study of these properties for regular surfaces, considering their classification via Kodaira dimension and Enriques-Kodaira types.
Findings
Preliminary analysis of the properties across surface classes
Identification of key cases based on Kodaira dimension
Foundational steps for further research
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.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometric Analysis and Curvature Flows · Meromorphic and Entire Functions