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A presentation for the mapping class group of a non-orientable surface from the action on the complex of curves
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Slope inequalities for fibred surfaces via GIT
Get PDFIn this paper we present a generalisation of a theorem due to Cornalba and Harris, which is an application of Geometric Invariant Theory to the study of invariants of fibrations. In particular, our generalisation makes it possible to treat the problem of bounding the invariants of general fibred surfaces. As a first application, we give a new proof of the slope inequality and of a bound for the invariants associated to double cover fibrations
On the class numbers of certain number fields obtained from points on elliptic curves II
Get PDFWe construct a family of cyclic extensions of number fields, in which every finite place is unramified, from an elliptic curve with a rational torsion point. As an application, we obtain such polynomials F(X) of rational coefficients that have the following property: For a rational number ξ chosen at random, the class number of the field generated by the square root of F(ξ) is “often” divisible by 3, 5 or by 7
The Glauberman correspondent of a nilpotent block of a finite group
Get PDFWe prove that a nilpotent block of a finite group and its Glauberman correspondent are basic Morita equivalent
