The Harbourne-Hirschowitz condition and the Anticanonical Orthogonal Property for surfaces

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.

13 pages, 1 figure. Minor changes