Vol. 89, No. 2, 1980

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Effective divisor classes and blowings-up of P2

Jeffrey Arthur Rosoff

Vol. 89 (1980), No. 2, 419–429
Abstract

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

[L ]2 = 1; [L]⋅[Ei] = 0; [Ei]⋅[Ej ] = − δi,j.

Let (Xn) 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
Authors
Jeffrey Arthur Rosoff