Reference material for lectures at the Syzygies and Free Resolutions workshop

CMI, December 2012

General reference is Algebraic Geometry by R. Hartshorne. More specific references are below.

  • Sheaves and Sheaves of modules: Chapter 2, Sections 1 and 5.
  • Divisors and line bundles on projective space: Chapter 2, Section 6.
  • Cohomology of sheaves: Chapter 3, Sections 1-2.
  • Cech complex and cohomology of Pn: Chapter 3, Sections 4-5.
  • Higher direct image sheaves: Chapter 3, Section 8.

    Other topics:

  • Regularity of coherent sheaves: Chapter 4 of Geometry of Syzygies by D. Eisenbud.
  • Np Property: Section 1.8.D in Positivity in Algebraic Geometry I by R. Lazarsfeld.
  • Grothendieck's theorem on splitting of vector bundles on P1: Theorem 2.1.1 in Vector Bundles on Complex Projective Spaces by C. Okonek, M. Schneider and H. Spindler.

    Lecture notes taken by Kavita Sutar (Thanks Kavita!):    Lectures 1-6   and    Lecture 7

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