Higher Genus Curves in Mathematical Physics and Arithmetic Geometry
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.
- Paperback | 222 pages
- 178 x 254 x 12.7mm | 340.19g
- 30 Apr 2018
- American Mathematical Society
- Providence, United States
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15 Sep 2009
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Table of contents
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.
About Andreas Malmendier
Tony Shaska, Oakland University, Rochester, MI.