Morse numbers of complex polynomials

To a complex polynomial function $f$ with arbitrary singularities we associate the number of Morse points in a general linear Morsification $f_t:=f-t\mathrm{\ell }$. We produce computable algebraic formulas in terms of invariants of $f$ for the numbers of stratwise Morse trajectories which abut, as $t\to 0$, to some point of the space or at infinity.