IJPAM: Volume 27, No. 2 (2006)

NASH MODIFICATIONS OF
REAL PROJECTIVE VARIETIES

E. Ballico
Department of Mathematics
University of Trento
380 50 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: [email protected]


Abstract.Let $X$ be an $n$-dimensional, $n \ge 3$, smooth projective variety defined over $\mathbb {R}$ such that $\mbox{\rm Pic}(X) \cong \mathbb {Z}$ and $H_1(X(\mathbb {C}),\mathbb {Z})=0$, and $d \ge 3$ an odd integer. Here we show how to construct a degree $d$ finite morphism $f: Y \to X$ defined over $\mathbb {R}$ and such that $Y$ has general type, $\mbox{\rm Pic}(Y) \cong \mathbb {Z}$, and no non-trivial automorphism.

Received: December 5, 2005

AMS Subject Classification: 14P05, 14P20

Key Words and Phrases: real algebraic variety, Nash morphism, sectional genus, finite morphism, étale morphism

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 27
Issue: 2