%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\documentclass{article}
\usepackage{amsthm,amsmath,amssymb,latexsym}
\pagestyle{empty}
\textwidth=12.8cm
\textheight=21.7cm
\hoffset=-0.3in
\voffset=-0.6in
\parskip=6pt
\lineskip=18pt
%------------------------------------------------------------
\begin{document}
\baselineskip=15pt

\centerline{\large \bf Are minimal rational curves determined by their tangent vectors?}

\bigskip

\centerline{Stefan Kebekus}
\centerline{\it Universit\"at Bayreuth.}


\bigskip
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\par
_
 Given a projective variety X and a dominating family H of rational
curves of minimal degrees, fix a general point x in X and consider a tangent
vector to X at x. In this setup, it is known by a previous work that only
finitely many members of H contain the given tangent direction --this can be
seen as an infinitesimal analogue to Mori's bend-and-break.

After a brief reiview of earlier results, we will show that -under suitable
conditions- at most one curve can contain the pre-given tangent vector. We
apply the result to irreducibility questions of families of rational curves of
minimal degrees.
\bigskip
\end{document}