2 00 1 On the hypersurface orbital varieties of sl ( N , C )

Quantization of Hypersurface Orbital Varieties in Sl N

The Topology of the Relative Character Varieties of a Quadruply-Punctured Sphere

Let M be a quadruply-punctured sphere with boundary components A; B; C; D. The SL(2; C)-character variety of M consists of equivalence classes of homomorphisms of 1 (M) ?! SL(2; C) and can be identiied with a quartic hypersurface in C 7. corresponding to representations with tr((A)) = a, tr((B)) = b, tr((C)) = c, tr((D)) = d is a cubic surface in C 3. We determine the singular

A geometric application of Nori’s connectivity theorem

Our main result in this paper concerns the problem of sweeping out general hypersurfaces of degree N ≥ d+ 2 in P : Theorem 1 Fix an integer 1 ≤ r ≤ d. Let γ = r−1 2 , r odd, or γ = r 2 , r even, that is γ is the round-up of r−1 2 . Let Y → S, dimS = C, be a family of r-dimensional smooth projective varieties. Then the general hypersurface of degree N in P is not rationally swept out by varietie...

Categorified quantum sl(2) and equivariant cohomology of iterated flag varieties

A 2-category was introduced in math.QA/0803.3652 that categorifies Lusztig’s integral version of quantum sl(2). Here we construct for each positive integer N a representation of this 2-category using the equivariant cohomology of iterated flag varieties. This representation categorifies the irreducible (N + 1)-dimensional representation of quantum sl(2).

Dense Orbits in Orbital Varieties in n Anna

Let O be a nilpotent orbit in the Lie algebra n( ) and let V be an orbital variety contained in O. Let P be the largest parabolic subgroup of SL(n, ) stabilizing V. We describe nilpotent orbits such that all the orbital varieties in them have a dense P orbit and show that for n big enough the majority of nilpotent orbits do not fulfill this. Résumé Soit O une orbite nilpotente dans l’algèbre de...