On non-proper intersections and local intersection numbers

• 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.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

NATURVETENSKAP  -- Matematik -- Algebra och logik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Algebra and Logic (hsv//eng)

TEKNIK OCH TEKNOLOGIER  -- Naturresursteknik -- Miljöledning (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Environmental Engineering -- Environmental Management (hsv//eng)

NATURVETENSKAP  -- Matematik -- Geometri (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Geometry (hsv//eng)

Keyword

segre numbers

Mathematics

Publication and Content Type

ref (subject category)

art (subject category)