On the Stable Reduction of Pencils of Curves.
In the current paper we show that the dimension of a family of irreducible reduced curves in a given ample linear system on a toric surface over an algebraically closed field is bounded from above by , where denotes a general curve in the family. This result generalizes a famous theorem of Zariski to the case of positive characteristic. We also explore new phenomena that occur in positive characteristic: We show that the equality does not imply the nodality of even if belongs to the...
Let be an algebraic projective smooth and trigonal curve of genus . In this paper we define, in a way equivalent to that followed by A. Maroni in [1], an integer , called the species of , which is a birational invariant having the property that and mod(2). In section 1 we prove that for every and every , as before, there are trigonal curves of genus and species . In section 2 we define the space of moduli of trigonal curves of genus and species . We note that is irreducible...