Non-reflexive projective curves of low degree.
Let X be a sufficiently general smooth k-gonal curve of genus g and R ∈ Pic(X) the degree k spanned line bundle. We find an optimal integer z > 0 such that the line bundle is very ample and projectively normal.
Let be a field of odd characteristic , let be an irreducible separable polynomial of degree with big Galois group (the symmetric group or the alternating group). Let be the hyperelliptic curve and its jacobian. We prove that does not have nontrivial endomorphisms over an algebraic closure of if either or .
We prove that a very ample special line bundle of degree on a general -gonal curve is normally generated if the degree of the base locus of its dual bundle does not exceed , where .