Quadratic Vector Fields in $\mathbb C\mathrm~P^2$ with Solvable Monodromy Group at Infinity

Quadratic vector fields for which the line at infinity is a phase curve with three different singular points are considered. It is assumed that the characteristic numbers of these singular points are not multiples of $1/4$ or $1/6$. It is shown that among the fields with fixed characteristic numbers satisfying this assumption, one can choose seven fields such that any other field with solvable noncommutative monodromy group at infinity is affine equivalent to one of the chosen fields. In addition, quadratic vector fields with commutative monodromy group at infinity are described.