Some explicit minimal graded free resolutions[HBNI Th2]

Abstract

This thesis has three parts. In the first part an irreducible curve C in P^2 is considered. The Veronese map is used for mapping it to P^5 and the resolutions are computed. In the second part, looking into two distinct irreducible plane projective curves and by Bezout's theorem the reduced intersection of two distinct curves, C and C' are considered in P^2, and found the resolution of sigma ( C intersection C' ). In the third part an explicit differential graded algebra is computed for one of the previously computed resolutions. While working on Syzygies and minimal free resolutions, only the homogeneous coordinate rings of projective varieties and finitely generated modules over them are considered and hence the definitions and notations adapted accordingly.