## Abstract

We give an elementary description of the maps in the linear strand of the minimal free resolution of a square-free monomial ideal, that is, the Stanley-Reisner ideal associated to a simplicial complex Δ. The description is in terms of the homology of the canonical Alexander dual complex Δ*. As applications we are able to • prove for monomial ideals and j = 1 a conjecture of J. Herzog giving lower bounds on the number of i-syzygies in the linear strand of j^{th}-syzygy modules. • show that the maps in the linear strand can be written using only ±1 coefficients if Δ* is a pseudomanifold, • exhibit an example where multigraded maps in the linear strand cannot be written using only ±1 coefficients. • compute the entire resolution explicitly when Δ* is the complex of independent sets of a matroid.

Original language | English (US) |
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Pages (from-to) | 117-132 |

Number of pages | 16 |

Journal | Mathematica Scandinavica |

Volume | 89 |

Issue number | 1 |

DOIs | |

State | Published - 2001 |