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Softcover ISBN:  9781470428563 
Product Code:  CONM/703 
List Price:  $130.00 
MAA Member Price:  $117.00 
AMS Member Price:  $104.00 
eBook ISBN:  9781470446741 
Product Code:  CONM/703.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9781470428563 
eBook ISBN:  9781470446741 
Product Code:  CONM/703.B 
List Price:  $255.00 $192.50 
MAA Member Price:  $229.50 $173.25 
AMS Member Price:  $204.00 $154.00 

Book DetailsContemporary MathematicsVolume: 703; 2018; 222 ppMSC: Primary 11; 14
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.
ReadershipGraduate students and research mathematicians interested in superelliptic and hypelliptic curves.

Table of Contents

Articles

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 MordellWeil rank $15$ revisited

Caleb McKinley Shor — Higherorder 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 — Selfinversive polynomials, curves, and codes

Anand Deopurkar and Anand Patel — Syzygy divisors on Hurwitz spaces


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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.
Graduate students and research mathematicians interested in superelliptic and hypelliptic curves.

Articles

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 MordellWeil rank $15$ revisited

Caleb McKinley Shor — Higherorder 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 — Selfinversive polynomials, curves, and codes

Anand Deopurkar and Anand Patel — Syzygy divisors on Hurwitz spaces