IJPAM: Volume 63, No. 3 (2010)

SEVERI VARIETIES, VARIETIES WITH AN APPARENT
DOUBLE POINT AND THE STRATIFICATION OF
$\mathbb {P}^n$ BY THEIR $X$-RANKS

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 an integral variety. For any $P\in \mathbb {P}^n$ the $X$-rank $r_X(P)$ is the minimal cardinality of a set $S\subset X$ such that $P\in \langle S\rangle$. Here we study the stratification of $\mathbb {P}^n$ when $X$ is a Severi variety or a smooth variety with only one apparent double point (OADP).

Received: January 18, 2010

AMS Subject Classification: 14N05

Key Words and Phrases: ranks, border ranks, extremal varieties, Severi varieties, variety with OADP

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 63
Issue: 3