Kirchhoff’s theorem for Prym varieties

• Published in: Forum of mathematics. Sigma Vol. 10
• Main Authors: Len, Yoav, Zakharov, Dmitry
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 01.01.2022
• Subjects: Algebra; Algebraic and Complex Geometry; Decomposition; Graphs; Theorems; Trees; 14T05; 14H40

We prove an analogue of Kirchhoff’s matrix tree theorem for computing the volume of the tropical Prym variety for double covers of metric graphs. We interpret the formula in terms of a semi-canonical decomposition of the tropical Prym variety, via a careful study of the tropical Abel–Prym map. In pa...