The Severi problem for rational curves on del Pezzo surfaces
Name
61214410-MIT.pdf
Description
Full printable version
Size
707.22 KB
Format
Adobe PDF
Checksum (MD5)
96cbcd9aee123ab96e5234167b9fbb9d
Author(s)
Testa, Damiano
Advisor(s)
Aise Johan de Jong.
Date Issued
2005
Publisher
Massachusetts Institute of Technology
Abstract
Let X be a smooth projective surface and choose a curve C on X. Let VC be the set of all irreducible divisors on X linearly equivalent to C whose normalization is a rational curve. The Severi problem for rational curves on X with divisor class [C] consists of studying the irreducibility of the spaces VC as C varies among all curves on X. In this thesis, we prove that all the spaces VC are irreducible in the case where X is a del Pezzo surface of degree at least two. If the degree of X is one, then we prove the same result only for a general X, with the exception of V-KX, where KX is the canonical divisor of X. It is well known that for general del Pezzo surface of degree one, V-KX consists of twelve points, and thus cannot be irreducible.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Includes bibliographical references (p. 141-142).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
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