48 research outputs found
Linear maps in minimal free resolutions of Stanley-Reisner rings
In this short note we give an elementary description of the linear part of
the minimal free resolution of a Stanley-Reisner ring of a simplicial complex
. Indeed, the differentials in the linear part are simply a compilation
of restriction maps in the simplicial cohomology of induced subcomplexes of
.
Along the way, we also show that if a monomial ideal has at least one
generator of degree , then the linear strand of its minimal free resolution
can be written using only coefficients.Comment: 7 pages, 1 figure. An error was found in the earlier version,
therefore a part of the paper has been remove