**Contemporary Mathematics**

Volume: 123;
1992;
278 pp;
Softcover

MSC: Primary 14;

Print ISBN: 978-0-8218-5131-9

Product Code: CONM/123

List Price: $60.00

AMS Member Price: $48.00

MAA Member Price: $54.00

**Electronic ISBN: 978-0-8218-7711-1
Product Code: CONM/123.E**

List Price: $60.00

AMS Member Price: $48.00

MAA Member Price: $54.00

# Enumerative Algebraic Geometry

Share this page *Edited by *
*Steven L. Kleiman; Anders Thorup*

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

## Enumerative Algebraic Geometry

- Contents ix10 free
- Preface xi12 free
- Hieronymus georg zeuthen (1839–1920) 114 free
- How many smooth plane cubics with given j-invariant are tangent to 8 lines in general position? 1528
- Triple and quadruple contact of plane curves 3144
- Secant lines of smooth projective curves: an infinitesimal study of the symmetric products 6174
- New bounds for fermat curves over finite fields 89102
- Discriminants and limits of duals of plane curves 99112
- On the inseparability of the gauss map 107120
- The Brill-Segre formula for families of curves 131144
- Duality for elliptic normal surface scrolls 149162
- A note on the Riemann-Kempf theorem for curves 161174
- On the geometry of nodal plane cubics: the condition p 169182
- Characteristic numbers of degeneracy loci 189202
- On Halphen's first formula 199212
- Negative intersection multiplicities on singular varieties 213226
- Triple contact formulas in P3 223236
- Elliptic quartic curves in a generic quintic threefold 247260
- Characteristic numbers of plane curves: An excess intersection theoretical approach 259272
- Degenerations of conormal varieties 267280