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What Determines an Algebraic Variety?

- (Ams-216)

  • Format
  • Bog, hardback
  • Engelsk

Beskrivelse

A pioneering new nonlinear approach to a fundamental question in algebraic geometryOne of the crowning achievements of nineteenth-century mathematics was the proof that the geometry of lines in space uniquely determines the Cartesian coordinates, up to a linear ambiguity. What Determines an Algebraic Variety? develops a nonlinear version of this theory, offering the first nonlinear generalization of the seminal work of Veblen and Young in a century. While the book uses cutting-edge techniques, the statements of its theorems would have been understandable a century ago; despite this, the results are totally unexpected. Putting geometry first in algebraic geometry, the book provides a new perspective on a classical theorem of fundamental importance to a wide range of fields in mathematics.Starting with basic observations, the book shows how to read off various properties of a variety from its geometry. The results get stronger as the dimension increases. The main result then says that a normal projective variety of dimension at least 4 over a field of characteristic 0 is completely determined by its Zariski topological space. There are many open questions in dimensions 2 and 3, and in positive characteristic.

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Detaljer
  • SprogEngelsk
  • Sidetal240
  • Udgivelsesdato23-10-2013
  • ISBN139780691246802
  • Forlag Princeton University Press
  • Nummer i serien216
  • FormatHardback
Størrelse og vægt
  • Vægt498 g
  • Dybde2 cm
  • coffee cup img
    10 cm
    book img
    15,6 cm
    23,5 cm

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