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A Lie-theoretic generalization of some Hilbert schemes
Oscar Kivinen
We define several versions of a class of varieties attached to a complex reductive Lie algebra , generalizing the Hilbert scheme of points on the p…
Discriminants and motivic integration
Oscar Kivinen, Alexei Oblomkov, Dimitri Wyss
We study invariants of a plane cuve singularity coming from motivic integration on symmetric powers of a formal deformation of . We show that a natural discriminant inte…
The Hilb-vs-Quot Conjecture
Oscar Kivinen, Minh-Tâm Quang Trinh
Let be the complete local ring of a complex plane curve germ and its normalization. We propose a "Hilb-vs-Quot" conjecture relating the virtual weight polynomials of the Hi…
The affine Springer fiber-sheaf correspondence
Eugene Gorsky, Oscar Kivinen, Alexei Oblomkov
Given a semisimple element in the loop Lie algebra of a reductive group, we construct a quasi-coherent sheaf on a partial resolution of the trigonometric commuting variety of the L…
Algebra and geometry of link homology
Eugene Gorsky, Oscar Kivinen, José Simental
These notes cover the lectures of the first named author at 2021 IHES Summer School on "Enumerative Geometry, Physics and Representation Theory" with additional details and referen…
Generalized affine Springer theory and Hilbert schemes on planar curves
Niklas Garner, Oscar Kivinen
We show that Hilbert schemes of planar curve singularities and their parabolic variants can be interpreted as certain generalized affine Springer fibers for , as defined by G…
Unramified affine Springer fibers and isospectral Hilbert schemes
Oscar Kivinen
For any connected reductive group over , we revisit Goresky-Kottwitz-MacPherson's description of the torus equivariant Borel-Moore homology of affine Springer fiber…
Quadratic ideals and Rogers-Ramanujan recursions
Yuzhe Bai, Eugene Gorsky, Oscar Kivinen
We give an explicit recursive description of the Hilbert series and Gröbner bases for the family of quadratic ideals defining the jet schemes of a double point. We relate these rec…
Homology of Hilbert schemes of reducible locally planar curves
Oscar Kivinen
Let be a complex, reduced, locally planar curve. We extend the results of Rennemo arXiv:1308.4104 to reducible curves by constructing an algebra acting on $V=\bigoplus_{n\g…