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arXiv · 1211.5798

Arc diagram varieties

Justyna Kosakowska·Markus Schmidmeier
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Abstract

Let $k$ be an algebraically closed field and $\alpha$, $\beta$, $\gamma$ be partitions. An algebraic group acts on the constructible set of short exact sequences of nilpotent $k$-linear operators of Jordan types $\alpha$, $\beta$, and $\gamma$, respectively; we are interested in the stratification given by the orbits in the case where all parts of $\alpha$ are at most 2. Geometric properties of the degeneration relation are controlled by the combinatorics of arc diagrams. The extended bubble sort algorithm is used to construct chains of orbits such that subsequent strata have dimension difference equal to one.

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BibTeXRIS

Justyna Kosakowska, Markus Schmidmeier. 2012-11-25. Arc diagram varieties. https://doi.org/10.1090/conm%2F607

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