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Thomae type formulae for singular Z_N curves

TitleThomae type formulae for singular Z_N curves
Publication TypeJournal Article
Year of Publication2006
AuthorsEnolski, VZ, Grava, T
JournalLett. Math. Phys. 76 (2006) 187-214

We give an elementary and rigorous proof of the Thomae type formula for singular $Z_N$ curves. To derive the Thomae formula we use the traditional variational method which goes back to Riemann, Thomae and Fuchs. An important step of the proof is the use of the Szego kernel computed explicitly in algebraic form for non-singular 1/N-periods. The proof inherits principal points of Nakayashiki\\\'s proof [31], obtained for non-singular ZN curves.


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