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Further Examples and Applications of Degree

  • Joe Harris
Part of the Graduate Texts in Mathematics book series (GTM, volume 133)

Abstract

Since finding out that a quadric surface Q ⊂3 is abstractly isomorphic to the product ℙ1 × ℙ1 we have observed a number of times that, in describing a curve C ⊂ Q, it is much more useful to give its bidegree (a, b) in ℙ1 × ℙ1 (that is, the bidegree of the bihomogeneous polynomial F defining it as a subvariety of ℙ1 ⊂ ℙ1) than to give just its degree as a curve in P3 (the reader can check this is just a + b). We ask now what are the analogous numerical invariants of a k-dimensional subvariety X ⊂ ℙ m × ℙ n in general.

Keywords

Inverse Image Plane Curve Hyperplane Section Determinantal Variety Fundamental Class 
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 1992

Authors and Affiliations

  • Joe Harris
    • 1
  1. 1.Department of MathematicsHarvard UniversityCambridgeUSA

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