Seminars

Title: Singularities of a rational curves and matrix representation

abstract:

Let $f_0,f_1,f2,f_3$ be $4$ homogeneous polynomials in $\KK[s,t]$ of the same
degree $d\geq 1$ such that $\gcd(f_0,f_1,f_2,f_3) \in \KK$ and consider the
regular map
\begin{eqnarray*}
\PP^1_{\KKb} & \xrightarrow{\phi} & \PP^n_{\KKb} \\
(s:t) & \mapsto & (f_0:f_1:...:f_n)(s,t).
\end{eqnarray*}
The image of $\phi$ is an algebraic curve $\Cc$ in $\PP^3_{\KKb}$ which is
usually called a \emph{rational} curve.
In my talk, we exploxe how to compute the singular points of $\Cc$ through its
matrix representation.