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Atlanta 2017

Minimal integral models of algebraic curves.

Joint Mathematics Meetings in Atlanta, GA, 

January 7, 2017


Tony Shaska (shaska AT Department of Mathematics and Statistics, Oakland University, Rochester, MI 48386


In the 1960’s, many mathematicians (Kodaira, N´eron, Raynaud, Tate, Lichtenbaum, Shafarevich, Lipman, and Deligne-Mumford) develop a very elegant theory of preferred integral models for curves and abelian varieties.  There are some very special integral models, called minimal regular proper models for curves and N´eron models for abelian varieties. Other models are minimal according to the height of the curve, discriminant, etc.  In this session we want to explore some of the classical theories of the second half of the XX century and recent developments of the last decades.  

Topics of the session include, but are not limited to:

  • Equations of curves over their field of moduli

  • Field of moduli versus the field of definition

  • Minimal models of hyperelliptic curves

  • Models of curves with minimal height

  • Neron-Tate models

  • Reduction theory of binary forms

  • Julia invariant of binary forms

  • Number of superelliptic curves with bounded Julia invariant

  • Moduli height of curves

  • Database of curves according to their moduli height

  • Twists of curves with bounded height

  • Minimal regular proper models of curves

  • Minimal Weierstrass models

  • others


  • J. Berg                 (Rice University)
  • L. Beshaj              (University of Texas at Austin)
  • M. Izquierdo         (Linkoping University, Sweden) 
  • D. Lorenzini          (University of Georgia)
  • A. Malmendier      (Utah State)
  • A. Obus                (University of Virginia)
  • E. Previato            (Boston University)
  • M. Rupert              (University of Idaho)
  • C. Shor                  (Western New England)
  • P. Srinivasan          (Georgia Tech)
  • A. Swaminathan     (Harvard University)
  • D. Zureick-Brown   (Emory University)

AMS Special Session on Minimal Integral Models of Algebraic Curves