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On the self-intersection cycle of surfaces and some classical formulas for their secant varieties
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Rüdiger Achilles
,
Mirella Manaresi
Published/Copyright:
April 14, 2010
Abstract
We study the relation between certain local and global numerical invariants of a projective surface given by the Stückrad–Vogel self-intersection cycle. In the smooth case we find a relation between the degrees of the tangent, the secant and the first polar variety which generalizes classical relations between the so-called elementary invariants of surfaces. For singular surfaces this relation involves also the contributions of singularities to the self-intersection cycle. In order to make the formula really effective for singular surfaces, we need to describe the movable part of the self-intersection cycle on the singular locus. This is done explicitly for a particular class of non-normal del Pezzo surfaces.
Received: 2009-08-10
Revised: 2009-10-22
Published Online: 2010-04-14
Published in Print: 2011-September
© de Gruyter 2011
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- On the self-intersection cycle of surfaces and some classical formulas for their secant varieties
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Keywords for this article
Self-intersection cycle;
singular surfaces;
ramification loci;
secant varieties
Articles in the same Issue
- Quantum unique ergodicity of Eisenstein series on the Hilbert modular group over a totally real field
- On the self-intersection cycle of surfaces and some classical formulas for their secant varieties
- Wolff potentials and the 3-d wave operator
- Statistics for low-lying zeros of symmetric power L-functions in the level aspect
- Simple Harish-Chandra modules, intermediate series modules, and Verma modules over the loop-Virasoro algebra
- On the classification of fake lens spaces
- Cohomology and removable subsets
