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Enumerative Algebraic Geometry
Edited by: Steven L. Kleiman and Anders Thorup
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Contemporary Mathematics
1992; 278 pp; softcover
Volume: 123
ISBN-10: 0-8218-5131-4
ISBN-13: 978-0-8218-5131-9
List Price: US$57
Member Price: US$45.60
Order Code: CONM/123
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1989 marked the 150th anniversary of the birth of the great Danish mathematician Hieronymus Georg Zeuthen. Zeuthen's name is known to every algebraic geometer because of his discovery of a basic invariant of surfaces. However, he also did fundamental research in intersection theory, enumerative geometry, and the projective geometry of curves and surfaces. Zeuthen's extraordinary devotion to his subject, his characteristic depth, thoroughness, and clarity of thought, and his precise and succinct writing style are truly inspiring.

During the past ten years or so, algebraic geometers have reexamined Zeuthen's work, drawing from it inspiration and new directions for development in the field. The 1989 Zeuthen Symposium, held in the summer of 1989 at the Mathematical Institute of the University of Copenhagen, provided a historic opportunity for mathematicians to gather and examine those areas in contemporary mathematical research which have evolved from Zeuthen's fruitful ideas. This volume, containing papers presented during the symposium, as well as others inspired by it, illuminates some currently active areas of research in enumerative algebraic geometry.

Table of Contents

  • S. L. Kleiman -- Hieronymus Georg Zeuthen (1839-1920)
  • P. Aluffi -- How many smooth plane cubics with given \(j\)-invariant are tangent to \(8\) lines in general position?
  • S. J. Colley and G. Kennedy -- Triple and quadruple contact of plane curves
  • M. Coppens and T. Johnsen -- Secant lines of smooth projective curves; an infinitesimal study of the symmetric products
  • A. Hefez and N. Kakuta -- New bounds for Fermat curves over finite fields
  • S. Katz -- Discriminants and limits of duals of plane curves
  • S. Kleiman and R. Piene -- On the inseparability of the Gauss map
  • D. Laksov and A. Thorup -- The Brill-Segre formula for families of curves
  • R. Mallavibarrena and R. Piene -- Duality for elliptic normal surface scrolls
  • A. Mattuck -- A note on the Riemann-Kempf theorem for curves
  • J. M. Miret and S. X. Descamps -- On the geometry of nodal plane cubics: the condition \(p\)
  • A. Parusinski and P. Pragacz -- Characteristic numbers of degeneracy loci
  • C. Procesi and S. X. Descamps -- On Halphen's first formula
  • P. Roberts -- Negative intersection multiplicities on singular varieties
  • F. Rosselló -- Triple contact formulas in \(\Bbb P^3\)
  • I. Vainsencher -- Elliptic quartic curves in a generic quintic threefold
  • L. J. van Gastel -- Characteristic numbers of plane curves; An excess intersection theoretical approach
  • L. J. van Gastel -- Degenerations of conormal varieties
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