arXiv subjects
Publications and source records attributed to J. Kuttler.
This paper studies the singularities of affine Schubert varieties in the affine Grassmannian (of type $\mathrm{A}^{(1)}_\ell$). For two classes of affine Schubert varieties, we determine the singular loci; and for one class, we also determine explicitly the tangent spaces at singular points. For a general affine Schubert variety, we give partial results on the singular locus.
Let G -> \GL(V) be a finite-dimensional linear representation of a reductive linear algebraic group G on a finite-dimensional vector space V, defined over an algebraically closed field of characteristic zero. The categorical quotient V//G carries a natural stratification, due to D. Luna. This paper addresses the following questions: (i) Is the Luna stratification of X intrinsic? That is, does every automorphism of V//G map each stratum to another stratum? (ii) Are the individual Luna strata in X intrinsic? That is, does every automorphism of V//G maps each stratum to itself? In general, the Luna stratification is not intrinsic. Nevertheless, we give positive answers to questions (i) and (ii) for large classes of interesting representations.
It is an open problem to determine the dimension of the space of homogeneous polynomials of a fixed degree vanishing at finitely many points in the projective plane to certain multiplicities. We present various aspects of this problem and a version of a known algorithm (originally due to M. Nagata) to compute this dimension for nine or less points. Our methods are completely elementary and only involve the representation theory of SL_2.