Global representation of Segre numbers by Monge-Amp\`ere products
| hal.structure.identifier | Department of Mathematical Sciences | |
| hal.structure.identifier | Department of Mathematical Sciences [Chalmers] | |
| dc.contributor.author | ANDERSSON, Mats | |
| hal.structure.identifier | Chalmers University of Technology [Göteborg] | |
| dc.contributor.author | ERIKSSON, Dennis | |
| hal.structure.identifier | Chalmers University of Technology [Göteborg] | |
| dc.contributor.author | KALM, Håkan Samuelsson | |
| hal.structure.identifier | Department of Mathematics | |
| hal.structure.identifier | Department of Mathematical Sciences [Chalmers] | |
| dc.contributor.author | WULCAN, Elizabeth | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | YGER, Alain | |
| dc.date | 2020 | |
| dc.date.accessioned | 2024-04-04T03:03:23Z | |
| dc.date.available | 2024-04-04T03:03:23Z | |
| dc.date.issued | 2020 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193067 | |
| dc.description.abstractEn | 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 $\mathcal{B}(X)$ 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 $\mathcal{B}$-analogues of classical intersection theoretic constructions: For an analytic subspace $V\subset X$ we define a $\mathcal{B}$-Segre class, which is an element of $\mathcal{B}(X)$ 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-Amp\`ere-type product. For regular embeddings we construct a $\mathcal{B}$-analogue of the Gysin morphism. | |
| dc.language.iso | en | |
| dc.title.en | Global representation of Segre numbers by Monge-Amp\`ere products | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1007/s00208-020-01973-y | |
| dc.subject.hal | Mathématiques [math]/Variables complexes [math.CV] | |
| dc.identifier.arxiv | 1812.03054 | |
| bordeaux.journal | Matematische Annalen | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01950853 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01950853v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Matematische%20Annalen&rft.date=2020&rft.au=ANDERSSON,%20Mats&ERIKSSON,%20Dennis&KALM,%20H%C3%A5kan%20Samuelsson&WULCAN,%20Elizabeth&YGER,%20Alain&rft.genre=article |
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