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On the singular locus of certain subvarieties of Springer fibers

On the singular locus of certain subvarieties of Springer fibers

Let x ∈ End(K n ) be an endomorphism such that x 2 = 0 (where K is an algebraically closed field).The corresponding Springer fiber F x is the algebraic variety of x-stable complete flags.In the present case, F x has a suitable decomposition into a finite number of orbits …