Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Geometry of the Severi variety


Authors: Steven Diaz and Joe Harris
Journal: Trans. Amer. Math. Soc. 309 (1988), 1-34
MSC: Primary 14H10
DOI: https://doi.org/10.1090/S0002-9947-1988-0957060-8
MathSciNet review: 957060
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: This paper is concerned with the geometry of the Severi variety $ W$ parametrizing plane curves of given degree and genus, and specifically with the relations among various divisor classes on $ W$. Two types of divisor classes on $ W$ are described: those that come from the intrinsic geometry of the curves parametrized, and those characterized by extrinsic properties such as the presence of cusps, tacnodes, hyperflexes, etc. The goal of the paper is to express the classes of the extrinsically defined divisors in terms of the intrinsic ones; this, along with other calculations such as the determination of the canonical class of $ W$, is carried out by using various enumerative techniques. One corollary is that the variety of nodal curves of given degree and genus in the plane is affine.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 14H10

Retrieve articles in all journals with MSC: 14H10


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1988-0957060-8
Article copyright: © Copyright 1988 American Mathematical Society