On non-proper intersections and local intersection numbers
Artikel i vetenskaplig tidskrift, 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.

Författare

Mats Andersson

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Algebra och geometri

Håkan Samuelsson

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Algebra och geometri

Elizabeth Wulcan

Chalmers, Matematiska vetenskaper, Algebra och geometri

Göteborgs universitet

Mathematische Zeitschrift

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

Vol. In Press

Ämneskategorier

Algebra och logik

Miljöledning

Geometri

DOI

10.1007/s00209-021-02816-5

Mer information

Senast uppdaterat

2021-08-19