On non-proper intersections and local intersection numbers
Journal article, 2021

Given equidimensional (generalized) cycles mu(1) and mu(2) on a complex manifold Y we introduce a product mu(1) lozenge Y mu(2) that is a generalized cycle whose multiplicities at each point are the local intersection numbers at the point. If Y is projective, then given a very ample line bundle L -> Y we define a product mu(1)circle L mu(2) whose multiplicities at each point also coincide with the local intersection numbers. In addition, provided that mu(1) and mu(2) are effective, this product satisfies a Bezout inequality. If i : Y -> P-N is an embedding such that i* O(1) = L, then mu(1)circle L mu(2) can be expressed as a mean value of Stuckrad-Vogel cycles on P-N. There are quite explicit relations between lozenge Y and circle L.

Author

Mats Andersson

University of Gothenburg

Chalmers, Mathematical Sciences, Algebra and geometry

Håkan Samuelsson

University of Gothenburg

Chalmers, Mathematical Sciences, Algebra and geometry

Elizabeth Wulcan

Chalmers, Mathematical Sciences, Algebra and geometry

University of Gothenburg

Mathematische Zeitschrift

0025-5874 (ISSN) 1432-8232 (eISSN)

Vol. In Press

Subject Categories

Algebra and Logic

Environmental Management

Geometry

DOI

10.1007/s00209-021-02816-5

More information

Latest update

8/19/2021