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How to make free resolutions with Macaulay2 Chris Peterson and Hirotachi Abo
 

Summary: How to make free resolutions with Macaulay2
Chris Peterson and Hirotachi Abo
1. What are syzygies?
Let k be a field, let R = k[x0, . . . , xn] be the homogeneous coordinate ring
of Pn
and let X be a projective variety in Pn
. Consider the ideal I(X) of X.
Assume that {f0, . . . , ft} is a generating set of I(X) and that each polynomial
fi has degree di. We can express this by saying that we have a surjective
homogenous map of graded S-modules:
t
i=0
R(-di) I(X),
where R(-di) is a graded R-module with grading shifted by -di, that is,
R(-di)k = Rk-di
.
In other words, we have an exact sequence of graded R-modules:
t
i=0 R(-di)
&&MMMMMMMMMM

  

Source: Abo, Hirotachi - Department of Mathematics, University of Idaho

 

Collections: Mathematics