IJPAM: Volume 63, No. 1 (2010)

POSTULATION OF GENERAL UNIONS OF LINES AND
LINEAR SPACES WITH GOOD COHOMOLOGY IN DEGREE 2

E. Ballico
Department of Mathematics
University of Trento
38 123 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: [email protected]


Abstract.Let $X\subset \mathbb {P}^n$ be a general union of linear spaces. Let $Y\subset X$ be the union of the components of dimension $\ge 2$. Here we prove that if $h^0(Y,\mathcal {O}_Y(2)) < \binom{n+2}{2}-9n$, then $X$ has maximal rank.

Received: May 12, 2010

AMS Subject Classification: 14N05

Key Words and Phrases: Hilbert function, unions of linear spaces, unions of lines, maximal rank

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 63
Issue: 1