Classical Zariski pairs with nodes

Abstract

In this thesis we study complex projective sextic curves with simple singularities. All curves constituting classical Zariski pairs, especially those with nodes, are enumerated and classified up to equisingular deformation. Every set of singularities constituting a classical Zariski pair gives rise to at most two families, called abundant and non-abundant except for one which gives rise to three families, one abundant and two conjugate non-abundant. This classification is done arithmetically with the aid of integral lattices and quadratic forms.