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Equations of loci in tables of commuting Jordan types

Banff International Research Station for Mathematical Innovation and Discovery

The Jordan type of a nilpotent matrix is the partition giving the sizes of the Jordan blocks in the normal Jordan form of the matrix. In this talk we discuss all partitions that have a fixed partition Q as the generic Jordan type in their nilpotent commutator. We report on a joint work with A. Iarrobino, B. Van Steirteghem and R. Zhao in which we provide a complete description of ball such partitions for a partition Q with at most two parts. In particular we arrange all such partitions in a table that we denote by T (Q). We then report on an ongoing joint project with M. Boij, A. Iarrobino, B. Van Steirteghem and R. Zhao in which we study the equations of loci in T (Q).

Mathematics; Commutative rings and algebras; Several complex variables and analytic spaces; Commutative algebra

video/mp4

Author affiliation: Union College

2016-09-13

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/59156

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/