Very ample line bundles on regular surfaces obtained by projection

[摘要] We work over an algebraically closed field of arbitrary characteristic. Let X subset of P-N be a smooth projective surface with very ample line bundle L := O-X (1), of degree d and sectional genus g. Consider the blowing-up sigma : (X) over cap -> X at distinct points x(1),..., x(m) epsilon X with the exceptional divisors E-1,..., E-m and let (L) over cap be the line bundle sigma*L circle times O ((X)) over cap(-E-1 - ... - E-m) on (X) over cap. The purpose here is to give a necessary and sufficient condition for G to be very ample in terms of the configuration of x1,..., x,, for surfaces with h I (X, OX) = 0 and to <= d - 2g - 1. The key tool for the proof is the linear projection from a point of X. As an application, we will determine some surfaces of sectional genus 2 or 3. (c) 2006 Elsevier Inc. All rights reserved.

[发布日期] 2006-12-15

[关键词] very ample line bundle;very ample divisor;regular surface;linear projection