| Summary: | 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 <inline-formula> <math display="inline"> <semantics> <mo>Δ</mo> </semantics> </math> </inline-formula>. Indeed, the differentials in the linear part are simply a compilation of restriction maps in the simplicial cohomology of induced subcomplexes of <inline-formula> <math display="inline"> <semantics> <mo>Δ</mo> </semantics> </math> </inline-formula>. Along the way, we also show that if a monomial ideal has at least one generator of degree 2, then the linear strand of its minimal free resolution can be written using only <inline-formula> <math display="inline"> <semantics> <mrow> <mo>±</mo> <mn>1</mn> </mrow> </semantics> </math> </inline-formula> coefficients.
|
|---|
