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Abstract Fano threefolds which are IP 1 -bundles on smooth projective surfaces have been classified by Szurek and Wiśniewski in (17). The aim of the present paper is to describe the quantum cohomology ring in these explicit cases.
Abstract For a subset of a Lie incidence geometry two intrinsic notions of independence are introduced. Also defined is the notion of a parabolic subspace. A classification is achieved for certain independent subgraphs of the point collinearity graph of the Lie incidence geometries A n,k , B n,n...
Abstract Let X be a (possibly singular) subvariety of a complex manifold M and Y a subvariety of X . We assume that Y is the intersection locus of X with a submanifold P ⊂ M and that this intersection is generically transversal. For such a pair ( X , Y ), we prove a generalization of the...
Abstract Two of the problems listed in (14, 74.17) ask to prove or disprove the following statements: A) For each differentiable planar map ƒ : IR 2 → IR 2 the set of all differentials defines a spread of IR 4 . B) If the differentials of a differentiable map ƒ : IR 2 → IR 2 define a spread...
Abstract The projection body is determined for selected three-dimensional convex bodies. The relationship between the volume of a convex body and the volume of its projection body is explored by calculating the value of an affine-invariant functional defined on the class of convex bodies, and...
Abstract We show that for every lattice packing of n -dimensional spheres there exists an ( n /log 2 ( n ))-dimensional affine plane which does not meet any of the spheres in their interior, provided n is large enough. Such an affine plane is called a free plane and our result improves on former...
Abstract We prove the following extension to twin buildings of a result for spherical buildings which appears in (11): to every weak twin building ∆, there is canonically associated a thick twin building ∆̄ whose Weyl group W (∆̄) can be considered as a reflection subgroup of the Weyl...
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