--*- M2 -*-

Title: Cohomology

Description:

cohomology and direct image sheaves

see

    http://front.math.ucdavis.edu/math.AG/0506391
    math.AG/0506391
    Title: Relative Beilinson Monad and Direct Image for Families of Coherent Sheaves
    Author: David Eisenbud, Frank-Olaf Schreyer 

    Eisenbud, Floystad, Schreyer: Sheaf cohomology and resolutions over the
    exterior algebra , Trans. Amer. Math. Soc. 355 (2003), 4397-4426,

    Sheaf Algorithms Using the Exterior Algebra, by Wolfram Decker and David Eisenbud
    http://www.math.uiuc.edu/Macaulay2/Book/

This would be good for someone who wants to learn the underlying (advanced) theory.

See the preliminary code in BGG.m2.

See also the code on Frank Schreyer's web site
(http://math.uni-sb.de/ag-schreyer/home/computeralgebra.htm) in
computingRpi_star.m2 associated with math.AG/0506391, which implements the
algorithm, but it needs to be put into a package form, with a general
interface.

=============================================================================

Proposed by: Wolfram Decker <decker@math.uni-sb.de>,
	     Frank Schreyer <schreyer@math.uni-sb.de>
Potential Advisor: Frank Schreyer
Project assigned to: Mike Stillman and David Eisenbud, March, 2009.
Current status: 

=============================================================================

Progress log: