The variety of pairs of commuting nilpotent matrices is irreducible

By V. Baranovsky. 2001

82 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Nilpotent commuting varieties of reductive Lie algebras (2003, background): “When applied to GL(n), our result in conjunction with an observation in [2] shows that the punctual (local) Hilbert scheme Hn ⊂ Hilb(P(2)) is irreducible over any algebraically closed field.”
On the irreducibility of commuting varieties of nilpotent matrices (2003, methodology): “We get as a consequence a proof of the irreducibility of the local Hilbert scheme of n points of a smooth algebraic surface over K if either charK = 0 or charK ≥ n 2 .”
Autoduality of compactified Jacobians for curves with plane singularities (2010, background): “ identify HilbS,0 with the scheme of codimension nideals in k[[x,y]]. Lemma 3.1 (J. Brian¸con). dim(HilbS,0) = n−1; HilbS,0 has a unique component of maximal dimension. Proof. See [8], [22], [27], or [7]. Remark. In fact, HilbS,0 is irreducible. However, we do not need this claim; without it, Lemma ”