The hyperelliptic locus

DOI10.1215/S0012-7094-94-07634-5zbMath0832.14020MaRDI QIDQ1804674

Cris Poor

Publication date: 5 March 1996

Published in: Duke Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

period matrixSchottky problemprincipally polarized abelian varietiestheta constanthyperelliptic Jacobian

Mathematics Subject Classification ID

Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Picard schemes, higher Jacobians (14K30) Jacobians, Prym varieties (14H40) Theta functions and curves; Schottky problem (14H42)

Related Items (14)

On different expressions for invariants of hyperelliptic curves of genus 3 ⋮ Dispersionless Hirota equations and the genus 3 hyperelliptic divisor ⋮ On Frobenius' theta formula ⋮ Binary forms and the hyperelliptic superstring ansatz ⋮ Abelian pole systems and Riemann-Schottky-type problems ⋮ The Scorza correspondence in genus 3 ⋮ Constructing genus-3 hyperelliptic Jacobians with CM ⋮ Filtration under a stepped dam and Riemann theta functions ⋮ Universal periods of hyperelliptic curves and their applications. ⋮ Hyperelliptic Simple Factors of J₀(N) with Dimension at Least 3 ⋮ Non-hyperelliptic modular Jacobians of dimension 3 ⋮ An inverse Jacobian algorithm for Picard curves ⋮ Modular invariants for genus 3 hyperelliptic curves ⋮ Genus 3 hyperelliptic curves with CM via Shimura reciprocity

Cites Work

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• Tata lectures on theta. I: Introduction and motivation: Theta functions in one variable. Basic results on theta functions in several variables. With the assistance of C. Musili, M. Nori, E. Previato, and M. Stillman
• Theta functions on Riemann surfaces
• Period relations for hyperelliptic Riemann surfaces
• Some Identities for Abelian Integrals
• Fay's Trisecant Formula and Cross-Ratios
• Lectures on Riemann Surfaces: Jacobi Varieties
• Tata lectures on theta. II: Jacobian theta functions and differential equations. With the collaboration of C. Musili, M. Nori, E. Previato, M. Stillman, and H. Umemura

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