The ramificant determinant

Authors

Kingshook Biswas, Indian Statistical Institute, Kolkata
Ricardo Pérez-Mar, CNRS Centre National de la Recherche Scientifique

Article Type

Research Article

Publication Title

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

Abstract

We give an introduction to the transalgebraic theory of simply connected log- Riemann surfaces with a finite number of infinite ramification points (transalgebraic curves of genus 0). We define the base vector space of transcendental functions and establish by elementary methods some transcendental properties. We introduce the Ramificant deter- minant constructed with transcendental periods and we give a closed-form formula that gives the main applications to transalgebraic curves. We prove an Abel-like theorem and a Torelli-like theorem. Transposing to the transalgebraic curve the base vector space of transcendental functions, they generate the structural ring from which the points of the transalgebraic curve can be recovered algebraically, including infinite ramification points.

DOI

10.3842/SIGMA.2019.086

Publication Date

1-1-2019

Comments

Open Access, Gold, Green

Recommended Citation

Biswas, Kingshook and Pérez-Mar, Ricardo, "The ramificant determinant" (2019). Journal Articles. 1011.
https://digitalcommons.isical.ac.in/journal-articles/1011