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Abstract: A free resolution of an ideal I generated by p monomials can be described using the simplicial chain maps of a simplex on p vertices. This resolution is called the Taylor resolution of the ideal and was constructed by Diana Taylor in her thesis (1966). Work of Bayer, Peeva and Sturmfels further established a criterion for deciding whether the simplicial chain maps of a  smaller simplicial complex on p vertices describes a free resolution of I, and since then there has been a significant amount of work on trimming down the Taylor resolution to simplicial resolutions that are minimal (for certain classes of ideals) or closer to being minimal.  In this talk we will discuss a class of simplicial complexes, indexed by the positive integers, where the r-th complex in this class supports a resolution of the r-th power of I^r, where I is a square-free monomial ideal.

 

This work is joint with Susan Cooper, Sabine El Khoury, Sara Faridi, Sara Mayes-Tang, Susan Morey, and Sandra Spiroff, and was started at the "Women in Commutative Algebra" workshop in Banff, 2019.

Notes 11.5 MB application/pdf

Simplicial Resolutions of Powers of Square-Free Monomial Ideals