Browsing by Subject "simple singularity"

Filter results by typing the first few letters
Now showing 1 - 2 of 2
  • Thumbnail Image
    ItemOpen Access
    Classical Zariski pairs with nodes
    (2008) Akyol, Ayşegül
    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.
  • Thumbnail Image
    ItemOpen Access
    Simple singular irreducible plane sextics
    (2013) Akyol, Ayşegül
    We consider irreducible complex plane projective curves of degree six with simple singular points only and classify such curves up to equisingular deformation. (We concentrate on the so-called non-special curves, as the special ones are already known). We list all sets of singularities realized by such curves, discuss their relation to the maximizing sets (i.e., those of total Milnor number 19), and, for each set of singularities found, describe the connected components of the moduli space. We also discuss the question of the realizability of a given set of singularities by a real curve.