Abstract
Since finding out that a quadric surface Q ⊂ ℙ3 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 ⊂ ℙm × ℙn in general.
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© 1992 Springer Science+Business Media New York
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Harris, J. (1992). Further Examples and Applications of Degree. In: Algebraic Geometry. Graduate Texts in Mathematics, vol 133. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2189-8_19
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DOI: https://doi.org/10.1007/978-1-4757-2189-8_19
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3099-6
Online ISBN: 978-1-4757-2189-8
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