Implementing the Kustin-Miller complex construction
The Kustin-Miller 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 Kustin-Miller complex and its implementation in the Macaulay2 package
Implementation of the Kustin-Miller 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 Kustin-Miller 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 Kustin-Miller complex
A. Kustin and M. Miller, Constructing big Gorenstein ideals from small ones, J. Algebra 85 (1983)}, 303-322.
Constructing new varieties
J. Neves and S. Papadakis, A construction of numerical Campedelli surfaces with ZZ/6 torsion, Trans. Amer. Math. Soc. 361 (2009), 4999-5021.
Stellar subdivision case
Cyclic polytopes case