Let R be a polynomial ring in r variables over an infinite field K, and denote by D a corresponding dual ring, upon which R acts as differential operators. We study type two graded level Artinian algebras A = R/I , having socle degree j. For each such algebra A, we consider the family of Artinian Gorenstein [AG] quotients of A having the same socle degree. By Macaulay duality, A corresponds to ...

We study partially hyperbolic diffeomorphisms satisfying a trapping property which makes them look as if they were Anosov at large scale. We show that, as expected, they share several properties with Anosov diffeomorphisms. We construct an expansive quotient of the dynamics and study some dynamical consequences related to this quotient.

1 13 4. Free rational curves 14 5. Uniruledness 16 5.1. Definitions equivalent to uniruledness 16 5.2. Examples and consequences of uniruledness 18 6. Rational connectivity 20 6.1. Definitions equivalent to rational connectivity 21 6.2. Rational chain-connectivity implies rational connectivity 22 6.3. Examples and consequences of rational connectivity 26 7. The MRC quotient 27 7.1. Quotients by...

We describe hypergeometric functions of Deligne-Mostow type for open subsets of the configuration space of six points on P, induced from those for seven points on P. The seven point ball quotient example DM(2, 1) does not appear on Mostow’s original list [9], but does appear on Thurston’s corrected version [12]. We show that DM(2, 1) is a finite cover of the moduli space of cubic surfaces MC en...

We study the notion of a strongly normal sequence in the dual E∗ of a Banach space E. In particular, we prove that the following three conditions are equivalent: (1) E∗ has a strongly normal sequence, (2) (E∗, σ(E∗, E)) has a Schauder basic sequence, (3) E has an infinite-dimensional separable quotient.

abstract. in this paper we study some relations between the power andquotient power graph of a finite group. these interesting relations motivateus to find some graph theoretical properties of the quotient power graphand the proper quotient power graph of a finite group g. in addition, weclassify those groups whose quotient (proper quotient) power graphs areisomorphic to trees or paths.

We prove that the Leray spectral sequence in rational cohomology for the quotient map U n,d → U n,d /G where U n,d is the affine variety of equations for smooth hypersurfaces of degree d in P n (C) and G is the general linear group, degenerates at E 2 .

We prove that the Leray spectral sequence in rational cohomology for the quotient map Un,d → Un,d/G where Un,d is the affine variety of equations for smooth hypersurfaces of degree d in P(C) and G is the general linear group, degenerates at E2. 2000 Math. Subj. Class. 14D20, 14L35, 14J70.