Seminar in Real and Complex Geometry

Thursday, February 22, 2018, 11:00-12:00, Schreiber building, room 209

Andrés Jaramillo (Tel Aviv)

Trigonal morsifications on Hirzebruch Surfaces


Consider $p$ and $q$ real polynomials in one variable of same degree $d$, having $d$ real simple roots. If $p-q$ has $d$ real simple roots, which are the possible configurations of its roots with respect to the roots of $p$ and $q$? We defined a morsification on a Hirzebruch surface $\Sigma_n$ as a curve with three components having $3n$ nodal points and intersecting every fiber of the ruling generically in three real points. We use trigonal curves and dessins in order to give an answer on how to construct all possible configurations for a degree $d$. Additionally, we show unicity for the configuration with a maximal number of adjacent roots of one of the polynomials $p$, $q$ or $p-q$.