type free resolutions of monomial ideals

Author:
Kohji Yanagawa

Journal:
Proc. Amer. Math. Soc. **127** (1999), 377-383

MSC (1991):
Primary 13D02, 13D03, 13H10

MathSciNet review:
1610805

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Abstract: Let be a monomial ideal of . Bayer-Peeva-Sturmfels studied a subcomplex of the Taylor resolution, defined by a simplicial complex . They proved that if is *generic* (i.e., no variable appears with the same non-zero exponent in two distinct monomials which are minimal generators), then is the *minimal* free resolution of , where is the *Scarf complex* of . In this paper, we prove the following: for a generic (in the above sense) monomial ideal and each integer , there is an *embedded* prime of . Thus a generic monomial ideal with no embedded primes is Cohen-Macaulay (in this case, is shellable). We also study a non-generic monomial ideal whose *minimal* free resolution is for some . In particular, we prove that if all associated primes of have the same height, then is Cohen-Macaulay and is pure and strongly connected.

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Additional Information

**Kohji Yanagawa**

Affiliation:
Graduate School of Science, Osaka University, Toyonaka, Osaka 560, Japan

Email:
yanagawa@math.sci.osaka-u.ac.jp

DOI:
http://dx.doi.org/10.1090/S0002-9939-99-04947-3

Keywords:
Monomial ideal,
generic monomial ideal,
Taylor complex,
Scarf complex,
primary decomposition,
minimal free resolution,
Cohen-Macaulay ring

Received by editor(s):
May 31, 1997

Communicated by:
Wolmer V. Vasconcelos

Article copyright:
© Copyright 1999
American Mathematical Society