160 citations · 693 across the 40 of their papers we have counts for
6 papers · 1 filter
Nice Initial Complexes of Some Classical Ideals
Aldo Conca, Serkan Hosten, Rekha R. Thomas
This is a survey article on Gorenstein initial complexes of extensively studied ideals in commutative algebra and algebraic geometry. These include defining ideals of Segre and Ver…
Computing Groebner Fans
Komei Fukuda, Anders N. Jensen, Rekha R. Thomas
This paper presents algorithms for computing the Groebner fan of an arbitrary polynomial ideal. The computation involves enumeration of all reduced Groebner bases of the ideal. Our…
The Circuit Ideal of a Vector Configuration
Tristram Bogart, Anders N. Jensen, Rekha R. Thomas
The circuit ideal, $\ica$, of a configuration $\A = \{\a_1, ..., \a_n\} \subset \Z^d$ is the ideal generated by the binomials ${\x}^{\cc^+} - {\x}^{\cc^-} \in \k[x_1, ..., x_n]$ as…
Reverse Lexicographic and Lexicographic Shifting
Eric Babson, Isabella Novik, Rekha R. Thomas
A short new proof of the fact that all shifted complexes are fixed by reverse lexicographic shifting is given. A notion of lexicographic shifting, $Δ_{\lex}$ -- an operation that t…
Computing Tropical Varieties
Tristram Bogart, Anders Jensen, David Speyer +2
The tropical variety of a -dimensional prime ideal in a polynomial ring with complex coefficients is a pure -dimensional polyhedral fan. This fan is shown to be connected in…
Moduli of McKay quiver representations I: the coherent component
Alastair Craw, Diane Maclagan, Rekha R. Thomas
For a finite abelian group G in GL(n,k), we describe the coherent component Y_theta of the moduli space M_theta of theta-stable McKay quiver representations. This is a not-necessar…