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Softcover ISBN:  9780821851319 
Product Code:  CONM/123 
List Price:  $130.00 
MAA Member Price:  $117.00 
AMS Member Price:  $104.00 
eBook ISBN:  9780821877111 
Product Code:  CONM/123.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9780821851319 
eBook ISBN:  9780821877111 
Product Code:  CONM/123.B 
List Price:  $255.00 $192.50 
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Book DetailsContemporary MathematicsVolume: 123; 1992; 278 ppMSC: Primary 14
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

Articles

Steven L. Kleiman — Hieronymus Georg Zeuthen (1839–1920) [ MR 1143544 ]

Paolo Aluffi — How many smooth plane cubics with given $j$invariant are tangent to $8$ lines in general position? [ MR 1143545 ]

Susan Jane Colley and Gary Kennedy — Triple and quadruple contact of plane curves [ MR 1143546 ]

Marc Coppens and Trygve Johnsen — Secant lines of smooth projective curves; an infinitesimal study of the symmetric products [ MR 1143547 ]

Abramo Hefez and Neuza Kakuta — New bounds for Fermat curves over finite fields [ MR 1143548 ]

Sheldon Katz — Discriminants and limits of duals of plane curves [ MR 1143549 ]

Steven Kleiman and Ragni Piene — On the inseparability of the Gauss map [ MR 1143550 ]

Dan Laksov and Anders Thorup — The BrillSegre formula for families of curves [ MR 1143551 ]

Raquel Mallavibarrena and Ragni Piene — Duality for elliptic normal surface scrolls [ MR 1143552 ]

Arthur Mattuck — A note on the RiemannKempf theorem for curves [ MR 1143553 ]

J. M. Miret and S. XambóDescamps — On the geometry of nodal plane cubics: the condition $p$ [ MR 1143554 ]

Adam Parusiński and Piotr Pragacz — Characteristic numbers of degeneracy loci [ MR 1143555 ]

C. Procesi and S. XambóDescamps — On Halphen’s first formula [ MR 1143556 ]

Paul Roberts — Negative intersection multiplicities on singular varieties [ MR 1143557 ]

Francesc Rosselló — Triple contact formulas in ${\bf P}^3$ [ MR 1143558 ]

Israel Vainsencher — Elliptic quartic curves in a generic quintic threefold [ MR 1143559 ]

Leendert J. van Gastel — Characteristic numbers of plane curves: an excess intersection theoretical approach [ MR 1143560 ]

Leendert J. van Gastel — Degenerations of conormal varieties [ MR 1143561 ]


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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.

Articles

Steven L. Kleiman — Hieronymus Georg Zeuthen (1839–1920) [ MR 1143544 ]

Paolo Aluffi — How many smooth plane cubics with given $j$invariant are tangent to $8$ lines in general position? [ MR 1143545 ]

Susan Jane Colley and Gary Kennedy — Triple and quadruple contact of plane curves [ MR 1143546 ]

Marc Coppens and Trygve Johnsen — Secant lines of smooth projective curves; an infinitesimal study of the symmetric products [ MR 1143547 ]

Abramo Hefez and Neuza Kakuta — New bounds for Fermat curves over finite fields [ MR 1143548 ]

Sheldon Katz — Discriminants and limits of duals of plane curves [ MR 1143549 ]

Steven Kleiman and Ragni Piene — On the inseparability of the Gauss map [ MR 1143550 ]

Dan Laksov and Anders Thorup — The BrillSegre formula for families of curves [ MR 1143551 ]

Raquel Mallavibarrena and Ragni Piene — Duality for elliptic normal surface scrolls [ MR 1143552 ]

Arthur Mattuck — A note on the RiemannKempf theorem for curves [ MR 1143553 ]

J. M. Miret and S. XambóDescamps — On the geometry of nodal plane cubics: the condition $p$ [ MR 1143554 ]

Adam Parusiński and Piotr Pragacz — Characteristic numbers of degeneracy loci [ MR 1143555 ]

C. Procesi and S. XambóDescamps — On Halphen’s first formula [ MR 1143556 ]

Paul Roberts — Negative intersection multiplicities on singular varieties [ MR 1143557 ]

Francesc Rosselló — Triple contact formulas in ${\bf P}^3$ [ MR 1143558 ]

Israel Vainsencher — Elliptic quartic curves in a generic quintic threefold [ MR 1143559 ]

Leendert J. van Gastel — Characteristic numbers of plane curves: an excess intersection theoretical approach [ MR 1143560 ]

Leendert J. van Gastel — Degenerations of conormal varieties [ MR 1143561 ]