Higher Genus Curves in Mathematical Physics and Arithmetic Geometry

Higher Genus Curves in Mathematical Physics and Arithmetic Geometry

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This volume contains the proceedings of the AMS Special Session on Higher Genus Curves and Fibrations in Mathematical Physics and Arithmetic Geometry, held on January 8, 2016, in Seattle, Washington.

Algebraic curves and their fibrations have played a major role in both mathematical physics and arithmetic geometry. This volume focuses on the role of higher genus curves; in particular, hyperelliptic and superelliptic curves in algebraic geometry and mathematical physics.

The articles in this volume investigate the automorphism groups of curves and superelliptic curves and results regarding integral points on curves and their applications in mirror symmetry. Moreover, geometric subjects are addressed, such as elliptic $K$3 surfaces over the rationals, the birational type of Hurwitz spaces, and links between projective geometry and abelian functions.
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Product details

  • Paperback | 222 pages
  • 178 x 254 x 12.7mm | 340.19g
  • Providence, United States
  • English
  • 1470428563
  • 9781470428563

Table of contents

J. Russell and A. Wootton, A lower bound for the number of finitely maximal $C_p$-actions on a compact oriented surface
S. A. Broughton, Galois action on regular dessins d'enfant with simple group action
D. Swinarski, Equations of Riemann surfaces with automorphisms
R. Hidalgo and T. Shaska, On the field of moduli of superelliptic curves
L. Beshaj, Minimal integral Weierstrass equations for genus 2 curves
L. Beshaj, R. Hidalgo, S. Kruk, A. Malmendier, S. Quispe, and T. Shaska, Rational points in the moduli space of genus two
C. Magyar and U. Whitcher, Strong arithmetic mirror symmetry and toric isogenies
A. Kumar and M. Kuwata, Inose's construction and elliptic $K$3 surfaces with Mordell-Weil rank 15 revisited
C. M. Shor, Higher-order Weierstrass weights of branch points on superelliptic curves
E. Previato, Poncelet's porism and projective fibrations
A. Levin, Extending Runge's method for integral points
D. Joyner and T. Shaska, Self-inversive polynomials, curves, and codes
A. Deopurkar and A. Patel, Syzygy divisors on Hurwitz spaces.
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About Andreas Malmendier

Andreas Malmendier, Utah State University, Logan, UT.

Tony Shaska, Oakland University, Rochester, MI.
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