Effective divisor classes and blowings-up of P²

Jeffrey Arthur Rosoff

Vol. 89 (1980), No. 2, 419–429

DOI: 10.2140/pjm.1980.89.419

Abstract

Let X_n P² be the monoidal transformation of the (complex) projective plane centered at distinct points P₁,…,P_n of P². We recall that the Néron-Severi group of X_n is freely generated by the divisor class [L] of the proper transform L of a line in P² and by the classes [E_i] of the “exceptional” fibers E_i over P_i; the intersection pairing is given by

Let ℳ(X_n) denote the monoid of elements F in the Néron-Severi group with the property that F contains an effective divisor.

Mathematical Subject Classification 2000

Primary: 14J17

Milestones

Received: 17 September 1979

Revised: 16 December 1979

Published: 1 August 1980