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The Hasse principle for lines on cubic surfaces

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Daniel Loughran (Hannover)

What
  • Seminar
When Sep 30, 2014
from 02:15 pm to 03:45 pm
Where Mainz, 04-432
Contact Name Ariyan Javanpeykar
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The classical Hasse principle states that a quadratic form over the rational numbers represents zero rationally if and only if it represents zero over every completion of the rational numbers.

In this talk we address the following problem: does there exist a cubic surface over the field of rational numbers which contains no rational line, yet contains a line over every completion of the rational numbers? That is, does a Hasse type principle hold for the collection of lines on a cubic surface?

In the talk we shall explain, amongst other things, how one can translate this into a problem in graph theory which can be tackled using a computer.

This is joint work with Joerg Jahnel.

 
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