Maps to Projective Space

  • Karen E. Smith
  • Lauri Kahanpää
  • Pekka Kekäläinen
  • William Traves
Part of the Universitext book series (UTX)

Abstract

One of the main goals of algebraic geometry is to understand the geometry of smooth projective varieties. For instance, given a smooth projective surface X, we can ask a host of questions whose answers might help illuminate its geometry. What kinds of curves does the surface contain? Is it covered by rational curves, that is, curves birationally equivalent to ℙ1? If not, how many rational curves does it contain, and how do they intersect each other? Or is it more natural to think of the surface as a family of elliptic curves (genus-1 Riemann surfaces) or as some other family? Is the surface isomorphic to ℙ2 or some other familiar variety on a dense set? What other surfaces are birationally equivalent to X? What kinds of automorphisms does the surface have? What kinds of continuously varying families of surfaces does it fit into?

Keywords

Vector Bundle Line Bundle Projective Space Algebraic Variety Global Section 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Karen E. Smith
    • 1
  • Lauri Kahanpää
    • 2
  • Pekka Kekäläinen
    • 3
  • William Traves
    • 4
  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA
  2. 2.Department of MathematicsUniversity of JyvaeskylaeJyvaeskylaeFinland
  3. 3.Department of Computer Science and Applied MathematicsUniversity of KuopioKuopioFinland
  4. 4.US Naval AcademyAnnapolisUSA

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