KustinMiller complex
Contents
Implementing the KustinMiller complex construction
Overview
The KustinMiller complex construction, due to A. Kustin and M. Miller, can be applied to a tuple of resolutions of Gorenstein rings with certain properties to obtain a new Gorenstein ring and a resolution of it. It gives a tool to construct and analyze Gorenstein rings of high codimension. We describe the KustinMiller complex and its implementation in the Macaulay2 package
Goal
Implementation of the KustinMiller complex associated to two resolutions of Gorenstein ring R/I and R/J (R a polynomial ring, I,J homogeneous ideals) with I contained in J and dim(R/J) = dim(R/I)1.
To Do List

Implement the differentials of the KustinMiller complex 
Implement the correct grading 
Add Tom example  Add Jerry example

Add Stellar subdivision example 
Add cyclic polytope example 
Use to SimplicialComplexes package for the examples 
Add to the simplicial complexes package a class Face  Minimalize the KustinMiller complex
References
General
A. Kustin and M. Miller, Constructing big Gorenstein ideals from small ones, J. Algebra 85 (1983)}, 303322.
Papadakis, KustinMiller unprojection with complexes, J. Algebraic Geometry 13 (2004) 249268}
Constructing new varieties
J. Neves and S. Papadakis, A construction of numerical Campedelli surfaces with ZZ/6 torsion, Trans. Amer. Math. Soc. 361 (2009), 49995021.
G. Brown, M. Kerber, M. Reid, Fano 3folds in codimension 4, Tom and Jerry, Part I
Stellar subdivision case
J. Boehm, S. Papadakis: Stellar subdivisions and StanleyReisner rings of Gorenstein complexes
Cyclic polytopes case
J. Boehm, S. Papadakis: On the structure of StanleyReisner rings associated to cyclic polytopes
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