Monomial ideals

Monomial Gorenstein ideals

✍ Henrik Bresinsky 📂 Article 📅 1979 🏛 Springer 🌐 English ⚖ 722 KB

Skeletons of monomial ideals

✍ Jürgen Herzog; Ali Soleyman Jahan; Xinxian Zheng 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 105 KB

## Abstract In analogy to the skeletons of a simplicial complex and their Stanley–Reisner ideals we introduce the skeletons of an arbitrary monomial ideal __I__ ⊂ __S__ = __K__ [__x__~1~, …, __x~n~__ ]. This allows us to compute the depth of __S__ /__I__ in terms of its skeleton ideals. We apply th

Blowing up monomial ideals

✍ Marc Levine 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 294 KB

Let k be a ÿeld. Spivakovsky's theorem on the solution of Hironaka's polyhedral game has been extended by Bloch to show that a morphism f : Z → S of ÿnite type k-schemes can be put in good position with respect to a normal crossing divisor @S on S by taking the proper transform with respect to an it

Generic and Cogeneric Monomial Ideals

✍ Ezra Miller; Bernd Sturmfels; Kohji Yanagawa 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 346 KB

Monomial ideals which are generic with respect to either their generators or irreducible components have minimal free resolutions encoded by simplicial complexes. There are numerous equivalent ways to say that a monomial ideal is generic or cogeneric. For a generic monomial ideal, the associated pri

Local Cohomology at Monomial Ideals

✍ Mircea Mustaţa 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 266 KB

We prove that if B ⊂ R = k[X 1 , . . . , Xn] is a reduced monomial ideal, then d] , R), where B [d] is the dth Frobenius power of B. We give two descriptions for H i B (R) in each multidegree, as simplicial cohomology groups of certain simplicial complexes. As a first consequence, we derive a relati

Monomial Buchsbaum ideals in ℙr

✍ Henrik Bresinsky 📂 Article 📅 1984 🏛 Springer 🌐 English ⚖ 927 KB