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Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
8
votes
Geometric motivation for the Stanley-Reisner correspondence
I think you're asking if there's a direct geometric relationship between an algebraic variety $X=V(I)$ (i.e., the zero set of an ideal $I$) and the Stanley-Reisner complex $\Delta_I$ or $\Delta_{in(I) …
6
votes
Reference for combinatorics of cell decomposition of the Hilbert scheme of points in the plane
Another reference for Hilbert schemes is chapter 18 of Miller and Sturmfels' book Combinatorial Commutative Algebra, although I don't think they address your question specifically.
It's hard to imagi …