Timeline of Abelian Varieties - Nineteenth Century

Nineteenth Century

  • 1826 Niels Henrik Abel, Abel-Jacobi map
  • 1827 inversion of elliptic integrals independently by Abel and Carl Gustav Jacob Jacobi
  • 1829 Jacobi, Fundamenta nova theoriae functionum ellipticarum, introduces four theta functions of one variable
  • 1835 Jacobi points out the use of the group law for diophantine geometry, in Du usu Theoriae Integralium Ellipticorum et Integralium Abelianorum in Analysi Diophantea
  • 1836-7 Friedrich Julius Richelot, the Richelot isogeny.
  • 1847 Adolph Göpel gives the equation of the Kummer surface
  • 1851 Johann Georg Rosenhain writes a prize essay on the inversion problem in genus 2.
  • c. 1850 Thomas Weddle - Weddle surface
  • 1856 Weierstrass elliptic functions
  • 1857 Bernhard Riemann lays the foundations for further work on abelian varieties in dimension > 1, introducing the Riemann bilinear relations and Riemann theta function.
  • 1865 Carl Johannes Thomae, Theorie der ultraelliptischen Funktionen und Integrale erster und zweiter Ordnung
  • 1866, Alfred Clebsch and Paul Gordan, Theorie der Abel'schen Functionen
  • 1869 Weierstrass proves an abelian function satisfies an algebraic addition theorem
  • 1879, Charles Auguste Briot, Théorie des fonctions abéliennes
  • 1880 In a letter to Richard Dedekind, Leopold Kronecker describes his Jugendtraum, to use complex multiplication theory to generate abelian extensions of imaginary quadratic fields
  • 1884 Sofia Kovalevskaya writes on the reduction of abelian functions to elliptic functions
  • 1888 Friedrich Schottky finds a non-trivial condition on the theta constants for curves of genus g = 4, launching the Schottky problem.
  • 1891 Appell–Humbert theorem of Paul Émile Appell and Georges Humbert, classifies the holomorphic line bundles on an abelian surface by cocycle data.
  • 1894 Die Entwicklung der Theorie der algebräischen Functionen in älterer und neuerer Zeit, report by Alexander von Brill and Max Noether
  • 1895 Wilhelm Wirtinger, Untersuchungen über Thetafunktionen, studies Prym varieties
  • 1897 H. F. Baker, Abelian Functions: Abel's Theorem and the Allied Theory of Theta Functions

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Famous quotes related to nineteenth century:

    “... the nineteenth century believed in science but the twentieth century does not. Not.”
    —Gertrude Stein (1874–1946)

    “I delight to come to my bearings,... not to live in this restless, nervous, bustling, trivial Nineteenth Century, but stand or sit thoughtfully while it goes by.”
    —Henry David Thoreau (1817–1862)

    “In the nineteenth century ... explanations of who and what women were focused primarily on reproductive events—marriage, children, the empty nest, menopause. You could explain what was happening in a woman’s life, it was believed, if you knew where she was in this reproductive cycle.”
    —Grace Baruch (20th century)

    “We have now traced the history of women from Paradise to the nineteenth century and have heard nothing through the long roll of the ages but the clank of their fetters.”
    —Jane, Lady Wilde (1821–1896)

    “Well, well, Henry James is pretty good, though he is of the nineteenth century, and that glaringly.”
    —Robert Louis Stevenson (1850–1894)