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Can anyone tell me where I may find an introduction to linear resolutions (of a $k[x_1,\ldots,x_n]$-module or ideal) including, of course, the standard definition of such a resolution, as well as its basic properties?

Thanks in advance.

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You can find some things about the linear free resolutions in the book of Bruns and Herzog, Cohen-Macaulay Rings. – user26857 Jul 11 '12 at 9:18
    
You can look into Graded Syzygies, by Irena Peeva – user89034 Jan 4 '14 at 19:19

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