Pluricanonical systems on surfaces with small K-2

摘要

We prove that the bicanonical system of a surface of general type with K-2 = 4 has no base components and we describe clusters contracted by 3K(X) and 4K(X) for regular surfaces with small K-X(2). In particular, we answer the question when 3K(X) or 4K(X) define embeddings of a canonical surface. [References: 24]