Very special divisors on 4-gonal real algebraic curves
Given a real curve, we study special linear systems called"very special"for which the dimension does not satisfy a Clifford type inequality. We classify all these very special linear systems when the gonality of the curve is small.
Abstract Let K / F be a Kummer cyclic extension of number fields. In the case when the degree is a prime number, Gomez Ayala gave an explicit criterion for the existence of a normal integral basis. More recently Ichimura proposed a generalization of that result for cyclic extensions of arbitrary degree, but we have found that Ichimura’s result is incorrect. In this paper we present a counter-example to Ichimura’s result as well as the correct generalization of Gomez Ayala’s result.