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(1) 4 is of the second kind, if given any point P on Vm, there exists a mero-morphic (q - 1)-form w, defined globally on Vm , such that 4 - dw is holomorphic in the neighborhood of P; (2) 4. is of the second kind if l = 0f frO where r is any q-cycle of Vm - W which bounds in Vm. Picard and Lefschetz both prove the equivalence of these ...
Sir William Vallance Douglas Hodge FRS FRSE [2] (/ h ɒ dʒ /; 17 June 1903 – 7 July 1975) was a British mathematician, specifically a geometer. [ 3 ] [ 4 ] His discovery of far-reaching topological relations between algebraic geometry and differential geometry —an area now called Hodge theory and pertaining more generally to Kähler ...
In mathematics, Hodge theory, named after W. V. D. Hodge, is a method for studying the cohomology groups of a smooth manifold M using partial differential equations.
For this paperback edition, Professor Sir Michael Atiyah has written a foreword that sets Hodges work in its historical context and relates it briefly to developments. First published in 1941,...
In mathematics, the Hodge star operator or Hodge star is a linear map defined on the exterior algebra of a finite-dimensional oriented vector space endowed with a nondegenerate symmetric bilinear form. Applying the operator to an element of the algebra produces the Hodge dual of the element. This map was introduced by W. V. D. Hodge.
W. V. D. Hodge, The Existence Theorem for Harmonic Integrals, Proceedings of the London Mathematical Society, Volume s2-41, Issue 1, 1936, Pages 483–496, https://doi.org/10.1112/plms/s2-41.6.483
“Hodge theory” refers to the way of doing complex algebraic geometry started by W. V. D. Hodge and S. Lefschetz in the 1920s and 1930s. More specifically, it refers to the applications of the “Hodge decomposition” to de Rham cohomology and the de Rham diferential graded algebra.
