1. CJM 2015 (vol 67 pp. 1201)
||Chern Classes of Splayed Intersections|
We generalize the Chern class relation for the transversal intersection
of two nonsingular
varieties to a relation for possibly singular varieties, under
a splayedness assumption.
We show that the relation for the Chern-Schwartz-MacPherson classes
holds for two splayed hypersurfaces in a nonsingular variety,
and under a `strong splayedness' assumption for more
general subschemes. Moreover, the relation is shown to hold for
the Chern-Fulton classes
of any two splayed subschemes.
The main tool is a formula for Segre classes of splayed
subschemes. We also discuss the Chern class relation under the
assumption that one of the
varieties is a general very ample divisor.
Keywords:splayed intersection, Chern-Schwartz-MacPherson class, Chern-Fulton class, splayed blowup, Segre class
2. CJM 1997 (vol 49 pp. 520)
||Classical orthogonal polynomials as moments |
We show that the Meixner, Pollaczek, Meixner-Pollaczek, the continuous
$q$-ultraspherical polynomials and Al-Salam-Chihara polynomials, in
certain normalization, are moments of probability measures. We use
this fact to derive bilinear and multilinear generating functions for
some of these polynomials. We also comment on the corresponding formulas
for the Charlier, Hermite and Laguerre polynomials.
Keywords:Classical orthogonal polynomials, \ACP, continuous, $q$-ultraspherical polynomials, generating functions, multilinear, generating functions, transformation formulas, umbral calculus
Categories:33D45, 33D20, 33C45, 30E05