Journal
ALGEBRAIC GEOMETRY
Volume 8, Issue 3, Pages 358-373Publisher
EUROPEAN MATHEMATICAL SOC-EMS
DOI: 10.14231/AG-2021-009
Keywords
Schottky problem; theta function
Categories
Funding
- National Science Foundation [DMS-1802116]
- PRIN 2015 Moduli spaces and Lie Theory and progetto di ateneo 2015 Moduli, deformazioni e superfici K3
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In the spirit of Riemann and Schottky, researchers provide an explicit weak solution to the Schottky problem for any genus g. By applying a specific Schottky-Jung proportionality, a collection of polynomials in genus g theta constants is constructed to include the locus of Jacobians of genus g curves as an irreducible component.
We give an explicit weak solution to the Schottky problem, in the spirit of Riemann and Schottky. For any genus g, we write down a collection of polynomials in genus g theta constants such that their common zero locus contains the locus of Jacobians of genus g curves as an irreducible component. These polynomials arise by applying a specific Schottky-Jung proportionality to an explicit collection of quartic identities for genus g - 1 theta constants.
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