On some generalizations of Jacobi's residue formula
On the complexity of parametrizing curves.
On the computation of Weierstrass gap sequences.
On the finiteness theorem for rational maps on a variety of general type.
Optimal degree construction of real algebraic plane nodal curves with prescribed topology. I. The orientable case.
We study a constructive method to find an algebraic curve in the real projective plane with a (possibly singular) topological type given in advance. Our method works if the topological model T to be realized has only double singularities and gives an algebraic curve of degree 2N+2K, where N and K are the numbers of double points and connected components of T. This degree is optimal in the sense that for any choice of the numbers N and K there exist models which cannot be realized algebraically with...