Abstract
This chapter focuses on the converse to Bezout’s Theorem in the general, locally Cohen-Macaulay and arithmetically Cohen-Macaulay cases respectively. More precisely, we examine the following question. Let X, Y be subvarieties of projective space and assume that
where the sum is taken over the irreducible components of X ∩ Y. Is it true that then the intersection is proper? However, we will see that this is not the case in general. The main result of Section 5.1 will be that the above equality holds if and only if the join variety has minimal dimension. In particular we are able to deduce a formula of Lazarsfeld from this.
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© 1999 Springer-Verlag Berlin Heidelberg
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Flenner, H., O’Carroll, L., Vogel, W. (1999). Converse to Bezout’s Theorem. In: Joins and Intersections. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03817-8_6
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DOI: https://doi.org/10.1007/978-3-662-03817-8_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08562-8
Online ISBN: 978-3-662-03817-8
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