Nonproper intersection products and generalized cycles
| dc.contributor.author | ANDERSSON, Mats | |
| dc.contributor.author | ERIKSSON, Dennis | |
| dc.contributor.author | SAMUELSSON KALM, Håkan | |
| dc.contributor.author | WULCAN, Elizabeth | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | YGER, Alain | |
| dc.date.accessioned | 2024-04-04T02:46:13Z | |
| dc.date.available | 2024-04-04T02:46:13Z | |
| dc.date.issued | 2021-06-29 | |
| dc.identifier.issn | 2199-675X | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191529 | |
| dc.description.abstractEn | Abstract We develop intersection theory in terms of the $${{\mathscr {B}}}$$ B -group of a reduced analytic space. This group was introduced in a previous work as an analogue of the Chow group; it is generated by currents that are direct images of Chern forms and it contains all usual cycles. However, contrary to Chow classes, the $${{\mathscr {B}}}$$ B -classes have well-defined multiplicities at each point. We focus on a $${{\mathscr {B}}}$$ B -analogue of the intersection theory based on the Stückrad–Vogel procedure and the join construction in projective space. Our approach provides global $${{\mathscr {B}}}$$ B -classes which satisfy a Bézout theorem and have the expected local intersection numbers. We also introduce $${{\mathscr {B}}}$$ B -analogues of more classical constructions of intersections using the Gysin map of the diagonal. These constructions are connected via a $${{\mathscr {B}}}$$ B -variant of van Gastel’s formulas. Furthermore, we prove that our intersections coincide with the classical ones on cohomology level. | |
| dc.language.iso | en | |
| dc.publisher | Springer | |
| dc.title.en | Nonproper intersection products and generalized cycles | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1007/s40879-021-00473-w | |
| dc.subject.hal | Mathématiques [math]/Variables complexes [math.CV] | |
| dc.identifier.arxiv | 1908.11759 | |
| bordeaux.journal | European Journal of Mathematics | |
| 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-03274407 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-03274407v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=European%20Journal%20of%20Mathematics&rft.date=2021-06-29&rft.eissn=2199-675X&rft.issn=2199-675X&rft.au=ANDERSSON,%20Mats&ERIKSSON,%20Dennis&SAMUELSSON%20KALM,%20H%C3%A5kan&WULCAN,%20Elizabeth&YGER,%20Alain&rft.genre=article |
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