  We consider the natural A-infinity structure on the Ext-algebra $Ext^*(G,G)$
associated with the coherent sheaf $G={\cal O}_C\oplus {\cal
O}_{p_1}\oplus...\oplus {\cal O}_{p_n}$ on a smooth projective curve $C$, where
$p_1,...,p_n\in C$ are distinct points. We study the homotopy class of the
product $m_3$. Assuming that $h^0(p_1+...+p_n)=1$ we prove that $m_3$ is
homotopic to zero if and only if $C$ is hyperelliptic and the points $p_i$ are
Weierstrass points. In the latter case we show that $m_4$ is not homotopic to
zero, provided the genus of $C$ is at least 2. In the case $n=g$ we prove that
the A-infinity structure is determined uniquely (up to homotopy) by the
products $m_i$ with $i\le 6$. Also, in this case we study the rational map
${\cal M}_{g,g}\to {\Bbb A}^{g^2-2g}$ associated with the homotopy class of
$m_3$. We prove that for $g\ge 6$ it is birational onto its image, while for
$g\le 5$ it is dominant. We also give an interpretation of this map in terms of
tangents to $C$ in the canonical embedding and in the projective embedding
given by the linear series $|2(p_1+...+p_g)|$.
