publication . Other literature type . Thesis . 2010 . Embargo end date: 14 May 2010

Models of genus one curves

Sadek, Mohammad;
English
  • Published: 14 May 2010
  • Publisher: Apollo - University of Cambridge Repository
  • Country: United Kingdom
Abstract
In this thesis we give insight into the minimisation problem of genus one curves defined by equations other than Weierstrass equations. We are interested in genus one curves given as double covers of P1, plane cubics, or complete intersections of two quadrics in P3. By minimising such a curve we mean making the invariants associated to its defining equations as small as possible using a suitable change of coordinates. We study the non-uniqueness of minimisations of the genus one curves described above. To achieve this goal we investigate models of genus one curves over Henselian discrete valuation rings. We give geometric criteria which relate these models to th...
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arXiv: Mathematics::Algebraic Geometry
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