Author:
Agostini Daniele,Çelik Türkü Özlüm,Struwe Julia,Sturmfels Bernd
Abstract
AbstractA theta surface in affine 3-space is the zero set of a Riemann theta function in genus 3. This includes surfaces arising from special plane quartics that are singular or reducible. Lie and Poincaré showed that any analytic surface that is the Minkowski sum of two space curves in two different ways is a theta surface. The four space curves that generate such a double translation structure are parametrized by abelian integrals, so they are usually not algebraic. This paper offers a new view on this classical topic through the lens of computation. We present practical tools for passing between quartic curves and their theta surfaces, and we develop the numerical algebraic geometry of degenerations of theta functions.
Publisher
Springer Science and Business Media LLC
Reference34 articles.
1. Agostini, D., Chua, L.: Computing theta functions with Julia. arXiv:1906.06507 (2019)
2. Andreotti, A.: On a theorem of Torelli. Am. J. Math. 80, 801–828 (1958)
3. Arbarello, E., Cornalba, M., Griffiths, P.A.: Geometry of Algebraic Curves, vol. II. Springer, Berlin (2011)
4. Balk, A., Ferapontov, E.: Invariants of 4-wave interactions. Phys. D 65, 274–288 (1993)
5. Bolognese, B., Brandt, M., Chua, L.: From curves to tropical Jacobians and back. In: Smith, G.G., Sturmfels, B. (eds.) Combinatorial Algebraic Geometry. Fields Institute Communications, vol. 80, pp 21–45. Springer, New York (2017)
Cited by
5 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献