Higher Genus Curves in Mathematical Physics and Arithmetic Geometry
About this Title
Andreas Malmendier, Utah State University, Logan, UT and Tony Shaska, Oakland University, Rochester, MI, Editors
Publication: Contemporary Mathematics
Publication Year: 2018; Volume 703
ISBNs: 978-1-4704-2856-3 (print); 978-1-4704-4674-1 (online)
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.
Graduate students and research mathematicians interested in superelliptic and hypelliptic curves.
Table of Contents
- Jacob Russell and Aaron Wootton – A lower bound for the number of finitely maximal $C_p$-actions on a compact oriented surface
- S. Allen Broughton – Galois action on regular dessins d’enfant with simple group action
- David Swinarski – Equations of Riemann surfaces with automorphisms
- Ruben Hidalgo and Tony Shaska – On the field of moduli of superelliptic curves
- Lubjana 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
- Christopher Magyar and Ursula Whitcher – Strong arithmetic mirror symmetry and toric isogenies
- Abhinav Kumar and Masato Kuwata – Inose’s construction and elliptic $K3$ surfaces with Mordell-Weil rank $15$ revisited
- Caleb McKinley Shor – Higher-order Weierstrass weights of branch points on superelliptic curves
- E. Previato – Poncelet’s porism and projective fibrations
- Aaron Levin – Extending Runge’s method for integral points
- David Joyner and Tony Shaska – Self-inversive polynomials, curves, and codes
- Anand Deopurkar and Anand Patel – Syzygy divisors on Hurwitz spaces