Browsing FAS Scholarly Articles by Keyword "elliptic curves"

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    • Cubic curves and totally geodesic subvarieties of moduli space 

      McMullen, Curtis T.; Mukamel, Ronen; Wright, Alex (Annals of Mathematics, Princeton U, 2017)
      In this paper we present the first example of a primitive, totally geodesic subvariety F⊂g,nF⊂Mg,n with dim(F)>1dim(F)>1. The variety we consider is a surface F⊂1,3F⊂M1,3 defined using the projective geometry of plane ...

    • Disparity in Selmer Ranks of Quadratic Twists of Elliptic Curves 

      Klagsbrun, Zev; Mazur, Barry Charles; Rubin, Karl (Princeton University, Department of Mathematics, 2013)
      We study the parity of 2-Selmer ranks in the family of quadratic twists of an arbitrary elliptic curve E over an arbitrary number field K. We prove that the fraction of twists (of a given elliptic curve over a fixed number ...