Resumen de Existence of coherent systems of rank two and dimension four

Montserrat Teixidor i Bigas

• We show that the moduli space of coherent systems of rank two and dimension four on a generic curve of genus at least two is nonempty for any value of the parameter when the BrillNoether number is at least one and the degree is odd or when the BrillNoether number is at least five and the degree is even. In all these cases there is one component of the moduli space of coherent systems of the expected dimension. The case of rank two and dimension four is particularly relevant as it is the first case that cannot be treated by reduction to smaller rank or dimension.