摘要
We carry out an analysis of the canonical system of a minimal complex surface S of general type with irregularity q > 0.Using this analysis,we are able to sharpen in the case q > 0 the well-known Castelnuovo inequality KS2≥3pg(S) + q(S)-7.Then we turn to the study of surfaces with pg=2q-3 and no fibration onto a curve of genus > 1.We prove that for q≥6 the canonical map is birational.Combining this result with the analysis of the canonical system,we also prove the inequality:KS2≥7χ(S) + 2.This improves an earlier result of Mendes Lopes and Pardini (2010).
We carry out an analysis of the canonical system of a minimal complex surface S of general type with irregularity q 0.Using this analysis,we are able to sharpen in the case q 0 the well-known Castelnuovo inequality KS2≥3pg（S） ＋ q（S）-7.Then we turn to the study of surfaces with pg=2q-3 and no fibration onto a curve of genus 1.We prove that for q≥6 the canonical map is birational.Combining this result with the analysis of the canonical system,we also prove the inequality：KS2≥7χ（S） ＋ 2.This improves an earlier result of Mendes Lopes and Pardini （2010）.
基金
supported by FCT (Portugal) through program POCTI/FEDER and Project PTDC/MAT/099275/2008
by MIUR (Italy) through project PRIN 2007 "Spazi di moduli e teorie di Lie"
