Proposes new potentiality conditions for 2D finite-gap Schrödinger operators and an approach to identify isoPrymians of smooth double coverings with multiple branch points.
A characterization of Prym varieties
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abstract
We prove that Prym varieties of algebraic curves with two smooth fixed points of involution are exactly the indecomposable principally polarized abelian varieties whose theta-functions provide explicit formulae for integrable 2D Schr\"odinger equation.
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2026 1verdicts
UNVERDICTED 1representative citing papers
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2-dimensional finite-gap Schr\"{o}dinger operator whose spectrum admits two involutions
Proposes new potentiality conditions for 2D finite-gap Schrödinger operators and an approach to identify isoPrymians of smooth double coverings with multiple branch points.