Tropical refined curve counting from higher genera and lambda classes
Sign Up to like & getrecommendations! Published in 2019 at "Inventiones Mathematicae"
DOI: 10.1007/s00222-018-0823-z
Abstract: Block and Göttsche have defined a q-number refinement of counts of tropical curves in $$\mathbb {R}^2$$R2. Under the change of variables $$q=e^{iu}$$q=eiu, we show that the result is a generating series of higher genus log… read more here.
Keywords: genera lambda; counting higher; tropical refined; curve counting ... See more keywords
Higher genera Catalan numbers and Hirota equations for extended nonlinear Schrödinger hierarchy
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DOI: 10.1007/s11005-021-01391-4
Abstract: We consider the Dubrovin–Frobenius manifold of rank 2 whose genus expansion at a special point controls the enumeration of a higher genera generalization of the Catalan numbers, or, equivalently, the enumeration of maps on surfaces,… read more here.
Keywords: extended nonlinear; dinger hierarchy; nonlinear schr; catalan numbers ... See more keywords
Rosenhain-Thomae formulae for higher genera hyperelliptic curves
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Nonlinear Mathematical Physics"
DOI: 10.1080/14029251.2018.1440744
Abstract: Rosenhain's famous formula expresses the periods of first kind integrals of genus two hyperelliptic curves in terms of θ-constants. In this paper we generalize the Rosenhain formula to higher genera hyperelliptic curves by means of… read more here.
Keywords: thomae formulae; rosenhain thomae; hyperelliptic curves; genera hyperelliptic ... See more keywords