IJPAM: Volume 47, No. 2 (2008)

CURVES IN GRASMANNIANS AND PROJECTIVE SPACES:
REDUCIBILITY OR IRREDUCIBILITY OF THE STRATA
WITH FIXED RESTRICTED TANGENT BUNDLE

E. Ballico
Department of Mathematics
University of Trento
380 50 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: ballico@science.unitn.it


Abstract.Let $C$ be a smooth curve of genus $g$ and $E$ a rank $n$ vector bundle on $C$. Let $X$ be an $n$-dimensional projective manifolds. Let $V(E)$ be the set of all morphisms $f: C \to X$ such that $E \cong f^\ast (TX)$ (the restricted tangent bundle). Here we study the irreducibility of $V(E)$ if either $X = \mathbb {P}^n$ or $n = r(m-r)$ and $X$ is the Grassmannian $G(r,m)$.

Received: July 28, 2008

AMS Subject Classification: 14N05, 14M15

Key Words and Phrases: restricted tangent bundle, Grassmannian

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 47
Issue: 2