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Sagar Kolte
Sagar Kolte
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Fulton's Book on intersection theory (Pg.223, theorem 12.3) asserts the following result:

For r pure dimensional schemes in P^n, whose co-dimensions add to at most n, the product of their degrees is at least as great as the sum of the degrees of the irreducible components of their intersection.

Under what conditions can we say that the product of the degrees of schemes is equal to the degrees of the irreducible components of the scheme?

Thanks.

Fulton's Book on intersection theory asserts the following result:

For r pure dimensional schemes in P^n, whose co-dimensions add to at most n, the product of their degrees is at least as great as the sum of the degrees of the irreducible components of their intersection.

Under what conditions can we say that the product of the degrees of schemes is equal to the degrees of the irreducible components of the scheme?

Thanks.

Fulton's Book on intersection theory (Pg.223, theorem 12.3) asserts the following result:

For r pure dimensional schemes in P^n, whose co-dimensions add to at most n, the product of their degrees is at least as great as the sum of the degrees of the irreducible components of their intersection.

Under what conditions can we say that the product of the degrees of schemes is equal to the degrees of the irreducible components of the scheme?

Thanks.

Source Link
Sagar Kolte
Sagar Kolte
  • 55
  • 1
  • 5

A Theorem in Intersection theory.

Fulton's Book on intersection theory asserts the following result:

For r pure dimensional schemes in P^n, whose co-dimensions add to at most n, the product of their degrees is at least as great as the sum of the degrees of the irreducible components of their intersection.

Under what conditions can we say that the product of the degrees of schemes is equal to the degrees of the irreducible components of the scheme?

Thanks.