scholarly journals Standard bases and geometric invariant theoryI. Initial ideals and state polytopes

1988 ◽  
Vol 6 (2-3) ◽  
pp. 209-217 ◽  
Author(s):  
David Bayer ◽  
Ian Morrison
Keyword(s):  
Geometric Invariant ◽  
Standard Bases ◽  
Initial Ideals ◽  
State Polytopes

scholarly journals A geometric invariant of virtual n-links

2020 ◽  
Vol 282 ◽  
pp. 107311
Author(s):  
Blake K. Winter
Keyword(s):  
Geometric Invariant

scholarly journals Perverse Schobers and Wall Crossing

2017 ◽  
Vol 2019 (18) ◽  
pp. 5777-5810 ◽  
Author(s):  
W Donovan
Keyword(s):  
Invariant Theory ◽  
Local System ◽  
Vector Spaces ◽  
Geometric Invariant ◽  
Perverse Sheaf ◽  
Derived Equivalences ◽  
Grothendieck Groups ◽  
Wall Crossing ◽  
Git Quotient ◽  
Cohomology Complex

Abstract For a balanced wall crossing in geometric invariant theory (GIT), there exist derived equivalences between the corresponding GIT quotients if certain numerical conditions are satisfied. Given such a wall crossing, I construct a perverse sheaf of categories on a disk, singular at a point, with half-monodromies recovering these equivalences, and with behaviour at the singular point controlled by a GIT quotient stack associated to the wall. Taking complexified Grothendieck groups gives a perverse sheaf of vector spaces: I characterize when this is an intersection cohomology complex of a local system on the punctured disk.

Rings, Ideals and Standard Bases

2002 ◽  
pp. 1-88 ◽  
Author(s):  
Gert-Martin Greuel ◽  
Gerhard Pfister
Keyword(s):  
Standard Bases

scholarly journals Fast screening of protein surfaces using geometric invariant fingerprints

2009 ◽  
Vol 106 (39) ◽  
pp. 16622-16626 ◽  
Author(s):  
S. Yin ◽  
E. A. Proctor ◽  
A. A. Lugovskoy ◽  
N. V. Dokholyan
Keyword(s):  
Geometric Invariant ◽  
Protein Surfaces ◽  
Fast Screening

scholarly journals Initial ideals of Pfaffian ideals

2020 ◽  
Vol 12 (1) ◽  
pp. 91-105
Author(s):  
Colby Long
Keyword(s):  
Initial Ideals

scholarly journals Face Numbers and Nongeneric Initial Ideals

10.37236/1882 ◽  
2006 ◽  
Vol 11 (2) ◽  
Author(s):  
Eric Babson ◽  
Isabella Novik
Keyword(s):  
Cyclic Group ◽  
Simple Proof ◽  
Prime Order ◽  
Necessary Conditions ◽  
Betti Numbers ◽  
Proper Action ◽  
Initial Ideals ◽  
The Face ◽  
Algebraic Shifting

Certain necessary conditions on the face numbers and Betti numbers of simplicial complexes endowed with a proper action of a prime order cyclic group are established. A notion of colored algebraic shifting is defined and its properties are studied. As an application a new simple proof of the characterization of the flag face numbers of balanced Cohen-Macaulay complexes originally due to Stanley (necessity) and Björner, Frankl, and Stanley (sufficiency) is given. The necessity portion of their result is generalized to certain conditions on the face numbers and Betti numbers of balanced Buchsbaum complexes.

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