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Scrolls over four dimensional varieties
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Andrea Luigi Tironi
Published/Copyright:
September 11, 2009
Abstract
We point out the relations between the classical and the adjunction-theoretic definition of scroll over varieties of dimension four. In particular, we prove that an adjunction-theoretic scroll of dimension greater than or equal to seven, polarized by a very ample line bundle, is also a classical scroll and that a classical scroll is an adjunction-theoretic scroll with a few exceptions.
Received: 2007-11-09
Revised: 2008-01-07
Published Online: 2009-09-11
Published in Print: 2010-January
© de Gruyter 2010
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Articles in the same Issue
- Secant dimensions of low-dimensional homogeneous varieties
- Peano differentiable extensions in o-minimal structures
- Global properties of codimension two spacelike submanifolds in Minkowski space
- Local recognition of the line graph of an anisotropic vector space
- Bicanonical map of surfaces with χ = 1 fibered by hyperelliptic curves of genus 3
- O(p + 1) × O(q + 1)-invariant (r – 1)-minimal hypersurfaces in Euclidean space
- Positivity in power series rings
- Scrolls over four dimensional varieties
- Nearly flag-transitive affine planes
Keywords for this article
Adjunction theory;
adjoint vector bundles;
Fano–Mori contraction;
extremal ray
Articles in the same Issue
- Secant dimensions of low-dimensional homogeneous varieties
- Peano differentiable extensions in o-minimal structures
- Global properties of codimension two spacelike submanifolds in Minkowski space
- Local recognition of the line graph of an anisotropic vector space
- Bicanonical map of surfaces with χ = 1 fibered by hyperelliptic curves of genus 3
- O(p + 1) × O(q + 1)-invariant (r – 1)-minimal hypersurfaces in Euclidean space
- Positivity in power series rings
- Scrolls over four dimensional varieties
- Nearly flag-transitive affine planes
