Created as a celebration of mathematical pioneer Emma Previato, this comprehensive book highlights the connections between algebraic geometry and integrable systems, differential equations, mathematical physics, and many other areas. The authors, many of whom have been at the forefront of research into these topics for the last decades, have all been influenced by Previato's research, as her collaborators, students, or colleagues. The diverse articles in the book demonstrate the wide scope of Previato's work and the inclusion of several survey and introductory articles makes the text accessible to graduate students and non-experts, as well as researchers. The articles in this second volume discuss areas related to algebraic geometry, emphasizing the connections of this central subject to integrable systems, arithmetic geometry, Riemann surfaces, coding theory and lattice theory.
Integrable Systems and Algebraic Geometry: Volume 2
Algebraic geometry: a celebration of Emma Previato's 65th birthday Ron Donagi and Tony Shaska; 1. Arithmetic analogues of Hamiltonian systems Alexandru Buium; 2. Algebraic spectral curves over Q and their tau-functions Boris Dubrovin; 3. Frobenius split anticanonical divisors Sandor J. Kovacs; 4. Halves of points of an odd degree hyperelliptic curve in its jacobian Yuri G. Zarhin; 5. Normal forms for Kummer surfaces Adrian Clingher and Andreas Malmendier; 6. -functions: old and new results V. M. Buchstaber, V. Z. Enolski and D. V. Leykin; 7. Bergman tau-function: from Einstein equations and Dubrovin-Frobenius manifolds to geometry of moduli spaces Dmitry Korotkin; 8. The rigid body dynamics in an ideal fluid: Clebsch top and Kummer surfaces Jean-Pierre Francoise and Daisuke Tarama; 9. An extension of Delsarte, Goethals and Mac Williams theorem on minimal weight codewords to a class of Reed-Muller type codes Cicero Carvalho and Victor G. L. Neumann; 10. A primer on Lax pairs L. M. Bates and R. C. Churchill; 11. Lattice-theoretic characterizations of classes of groups Roland Schmidt; 12. Jacobi inversion formulae for a curve in Weierstrass normal form Jiyro Komeda and Shigeki Matsutani; 13. Spectral construction of non-holomorphic Eisenstein-type series and their Kronecker limit formula James Cogdell, Jay Jorgenson and Lejla Smajlovic; 14. Some topological applications of theta functions Mauro Spera; 15. Multiple Dedekind zeta values are periods of mixed Tate motives Ivan Horozov; 16. Noncommutative cross-ratio and Schwarz derivative Vladimir Retakh, Vladimir Rubtsov and Georgy Sharygin.