The Szeg\"o curve and Laguerre polynomials with large negative parameters

We study the asymptotic zero distribution of the rescaled Laguerre polynomials, ${\displaystyle L_n^{({\alpha }_n)}(nz)}$, with the parameter ${\alpha }_n$ varying in such a way that $\displaystyle \lim_{n\rightarrow \infty}\alpha_n/n=-1$. The connection with the so-called Szeg"{o} curve will be showed.