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Global representati...
Global representation of Segre numbers by Monge–Ampère products
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- Andersson, Mats, 1957 (author)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences
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- Eriksson, Dennis, 1981 (author)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences
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- Samuelsson, Håkan, 1976 (author)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences
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- Wulcan, Elizabeth, 1978 (author)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences
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- Yger, Alain (author)
- Université de Bordeaux,University of Bordeaux
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(creator_code:org_t)
- 2020-03-10
- 2021
- English.
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In: Mathematische Annalen. - : Springer Science and Business Media LLC. - 0025-5831 .- 1432-1807. ; 380:1-2, s. 349-391
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Abstract
Subject headings
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- On a reduced analytic space X we introduce the concept of a generalized cycle, which extends the notion of a formal sum of analytic subspaces to include also a form part. We then consider a suitable equivalence relation and corresponding quotient B(X) that we think of as an analogue of the Chow group and a refinement of de Rham cohomology. This group allows us to study both global and local intersection theoretic properties. We provide many B-analogues of classical intersection theoretic constructions: For an analytic subspace V⊂ X we define a B-Segre class, which is an element of B(X) with support in V. It satisfies a global King formula and, in particular, its multiplicities at each point coincide with the Segre numbers of V. When V is cut out by a section of a vector bundle we interpret this class as a Monge–Ampère-type product. For regular embeddings we construct a B-analogue of the Gysin morphism.
Subject headings
- NATURVETENSKAP -- Matematik -- Algebra och logik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Algebra and Logic (hsv//eng)
- NATURVETENSKAP -- Matematik -- Geometri (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Geometry (hsv//eng)
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Publication and Content Type
- art (subject category)
- ref (subject category)
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