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Cones of Curves and of Line Bundles on Surfaces Associated with Curves Having one Place at Infinity
Author(s) -
Campillo Antonio,
Piltant Olivier,
RegueraLópez Ana J.
Publication year - 2002
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611502013394
Subject(s) - mathematics , pencil (optics) , pure mathematics , sheaf , projective line , line at infinity , ample line bundle , elliptic curve , mathematical analysis , projective space , projective test , mechanical engineering , engineering
Let V be a pencil of curves in P 2 with one place at infinity, and X → P 2 the minimal composition of point blow‐ups eliminating its base locus. We study the cone of curves and the cones of numerically effective and globally generated line bundles on X. It is proved that all of these cones are regular. In particular, this result provides a new class of rational projective surfaces with a rational polyhedral cone of curves. The surfaces in this class have non‐numerically effective anticanonical sheaf if the pencil is neither rational nor elliptic. An application is a global version on X of Zariski's unique factorization theorem for complete ideals. We also define invariants of the semigroup of globally generated line bundles on X depending only on the topology of V at infinity. 2000 Mathematical Subject Classification : primary 14C20; secondary 14E05.