Generic properties of the adjuction mapping for singular surfaces and applications

Marco Andreatta, Mauro Beltrametti and Andrew Sommese

Vol. 142 (1990), No. 1, 1–15

DOI: 10.2140/pjm.1990.142.1

Abstract

In the last years many new results on the classical problem of classifying smooth surfaces in the projective space in terms of their extrinsic projective and intrinsic geometric invariants have been made by using the adjunction mapping. In this paper we extend the existence theorem for the adjunction mapping to the case of singular surfaces. Although the mapping is only meromorphic we obtain many inequalities known previously only in the smooth case. As an illustration of the results we given a very complete answer in the singular case, parallel to the smooth result, to the question of when a singular surface can “have a hyperelliptic hyperplane section”.

Mathematical Subject Classification 2000

Primary: 14C20

Secondary: 14J25

Milestones

Received: 25 January 1988

Published: 1 March 1990