IJPAM: Volume 95, No. 2 (2014)

POSTULATION OF DOUBLE POINTS WITH RESTRICTED
SUPPORT: THE CASE OF A SMOOTH QUADRIC 3-FOLD

E. Ballico
Department of Mathematics
University of Trento
38 123 Povo (Trento) - Via Sommarive, 14, ITALY


Abstract. Let $D$ be an integral hypersurface of the projective variety, $D\subset X$ a hypersurface and $L$ a line bundle on $X$. Let $E_{x,y}\subset X$ be a general union of $x$ double points of $X$ and $y$ double points of $X$. We classifies the triple $(L,x,y)$ for which $h^1(\mathcal {I}_{E_{x,y}}\otimes L)\cdot h^0(\mathcal {I}_{E_{x,y}}\otimes L)>0$ when $X$ is a smooth quadric 3-fold and $D$ is a hyperplane section of $X$ and in some cases with $X$ an integral quadric surface.

Received: April 21, 2014

AMS Subject Classification: 14N05, 15A69

Key Words and Phrases: quadric 3-fold; interpolation, double point, zero-dimensional scheme, secant variety

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DOI: 10.12732/ijpam.v95i2.7 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 95
Issue: 2
Pages: 209 - 221


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