On the Galois groups of the dualizing coverings for plane curves

Abstract

Let $C_1$ be an irreducible component of a reduced projective curve $C\subset {\mathbb{P}}^2$ defined over the field $\mathbb{C}$, $\mathrm{deg}{C}_1\ge 2$, and let $T$ be the set of lines $l\subset {\mathbb{P}}^2$ meeting $C$ transversally. In the article, we prove that for a line $l_0\in T$ and any two points $P_1,P_2\in C_1\cap l_0$ there is a loop $l_t\subset T$, $t\in [0,1]$, such that the movement of the line $l_0$ along the loop $l_t$ induces the transposition of the points $P_1$, $P_2$ and the identity permutation of the other points of $C\cap l_0$.

arXiv comment10 pages