An asymptotic existence theorem for plane curves with prescribed singularities

New Asymptotics for the Existence of Plane Curves with Prescribed Singularities

We study the classical problem of the existence of irreducible plane curves with given degree d and prescribed singularities of topological types S1 ; : : : ; Sr. Our main results concern substantial improvements of the leading coeecients in the asymptotically optimal suucient conditions for complex plane curves which were found in GLS1]. We then transfer these results to real plane curves.

On the Existence of Plane Curves with Prescribed Singularities

Infinite product representation of solution of indefinite SturmLiouville problem

In this paper, we investigate infinite product representation of the solution of a Sturm- Liouville equation with an indefinite weight function which has two zeros and/or singularities in a finite interval. First, by using of the asymptotic estimates provided in [W. Eberhard, G. Freiling, K. Wilcken-Stoeber, Indefinite eigenvalue problems with several singular points and turning points, Math. N...

On the Brill-Noether theory of curves in a weighted projective plane

We study the gonality and the existence of low degree pencils on curves with a model on a weighted projective plane, when their singularities are only ordinary nodes or ordinary cusps and they are general in the weighted projective plane. M.S.C. 2010: 14H51, 14J26.

Global classification of curves on the symplectic plane

In [17], we considered the local classification of plane curves on the symplectic plane. In particular, we introduced the number “symplectic defect”, which represents the difference of two natural equivalence relations on plane curves, the equivalence by diffeomorphisms and that by symplectomorphisms. For an immersion, two equivalence relations coincide, so the symplectic defect is null. For co...