Year: 2026
Type: article
Abstract: We compute the algebraic equation for arctic curves of the Aztec diamond with a doubly (quasi-)periodic weight structure and obtain similar results for certain models of the hexagon. In particular, we determine the algebraic degree of such curves as a function of the number of frozen and smooth (or gaseous) regions. The key to our result is the construction of a discriminant for meromorphic differentials on a higher genus Riemann surface. This construction works analogously for meromorphic sections of arbitrary holomorphic line bundles. In the genus $$g = 0$$ g = 0 case this notion reduces to the usual discriminant of a polynomial.
Source: Selecta Mathematica
Author: Mateusz Piorkowski
Institution: Durham University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W4404261723