146 citations · 286 across the 20 of their papers we have counts for
5 papers · 2 filters
Symbolic powers of monomial ideals and vertex cover algebras
Juergen Herzog, Takayuki Hibi, Ngo Viet Trung
We introduce and study vertex cover algebras of weighted simplicial complexes. These algebras are special classes of symbolic Rees algebras. We show that symbolic Rees algebras of…
A generalization of the Taylor complex construction
Juergen Herzog
Given multigraded free resolutions of two monomial ideals we construct a multigraded free resolution of the sum of the two ideals.
The strong Lefschetz property and simple extensions
Juergen Herzog, Dorin Popescu
Stanley showed that monomial complete intersections have the strong Lefschetz property. Extending this result we show that a simple extension of an Artinian Gorenstein algebra with…
Notes on the multiplicity conjecture
Juergen Herzog, Xinxian Zheng
New cases of the multiplicity conjecture are considered.
Finite Filtrations of Modules and Shellable Multicomplexes
Juergen Herzog, Dorin Popescu
We introduce pretty clean modules, extending the notion of clean modules by Dress, and show that pretty clean modules are sequentially Cohen-Macaulay. We also extend a theorem of D…