On the Manin conjectures for singular cubic hypersurfaces (40')
speaker: Per Salberger (Chalmers University of Technology, Gothenburg)abstract: We consider non-conical cubic hypersurfaces with singular locus of codimension at least two. Such hypersurfaces have at worst canonical singularites. One may therefore, following Batyrev and Tschinkel, apply the minimal model program and give a precise conjecture for the asymptotics of the rational points of bounded height. If X is non-singular or has a crepant resolution, one recovers the conjectures of Manin or Peyre.
There have been a number of papers on these conjectures for singular cubic surfaces, but very few results for cubic threefolds or fourfolds. We have recently in joint work with V. Blomer and J. Brüdern proven a strong form of the Manin-Peyre conjecture for a certain singular cubic fourfold. We describe in our talk the geometric parts of this work like the use of descent theory (universal torsors) over a crepant resolution of the fourfold.
timetable:
Thu 18 Oct, 15:30 - 16:10, Sala Conferenze Centro De Giorgi
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