Displaying similar documents to “Riemann surfaces with a large abelian group of automorphisms.”

On surfaces of general type with p = q = 1, K = 3.

Francesco Polizzi (2005)

Collectanea Mathematica

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The moduli space M of surfaces of general type with p = q = 1, K = g = 3 (where g is the genus of the Albanese fibration) was constructed by Catanese and Ciliberto in [14]. In this paper we characterize the subvariety M ⊂ M corresponding to surfaces containing a genus 2 pencil, and moreover we show that there exists a non-empty, dense subset M ⊂ M which parametrizes isomorphism classes of surfaces with birational bicanonical map.

Five-gonal curves of genus nine.

Marc Coppens (2005)

Collectanea Mathematica

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Let C be a smooth 5-gonal curve of genus 9. Assume all linear systems g on C are of type I (i.e. they can be counted with multiplicity 1) and let m be the numer of linear systems g on C. The only possibilities are m=1; m=2; m=3 and m=6. Each of those possibilities occur.

A generalization of the Nikodym boundedness theorem.

Christopher Stuart (2007)

Collectanea Mathematica

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In this note an internal property of a ring of sets, named the Nested Partition Property, is shown to imply the Nikodym Property. A wide range of examples are shown to have this property.