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HigherCIOperators :: HigherCIOperators

HigherCIOperators -- "Higher CI operators on a resolution over a complete intersection"

Description

The "higher CI operators" complete the structure of the ordinary CI operators on (sometimes called "Eisenbud operators") on a resolution over a complete intersection in the same sense that the "higher homotopies" complete the structure of homotopies on with respect to a sequence of elements. Details will appear in a preprint in preparation by Burke, Eisenbud and Schreyer.

The higher CI operators are constructed by the routine higherCIOperators.

Just as a system of higher homotopies for a regular sequence f1..fc on a resolution over a ring S allow one to construct the Shamash resolution over R = S/(f1..fc), the higher CI operators are involved in a sort of dual construction: from a resolution F over R, lifted to a sequence of maps A over S, and lifted higher CI operators on A⊗L, where L is the Koszul complex on f, one can construct a nonminimal resolution AL over S using the routine ciOperatorResolution.

Author

Version

This documentation describes version 0.5 of HigherCIOperators.

Source code

The source code from which this documentation is derived is in the file HigherCIOperators.m2.

Exports