Regularity and Multisecant Lines of Finite Schemes

Abstract

For a nondegenerate finite subscheme Gamma in P-c, let reg(Gamma) and l (Gamma) be, respectively, the regularity of Gamma and the largest integer l such that there exists an l-secant line to Gamma. It is always true that reg(Gamma) >= l (Gamma). In this article, we show that if reg(Gamma) >= d-c+5/2 then reg(Gamma) is equal to l (Gamma). In addition, we describe the minimal free resolution of the homogeneous ideal of Gamma for the case reg(Gamma) >= d-c+5/2.