Residual intersection (original) (raw)
In algebraic geometry, the problem of residual intersection asks the following: Given a subset Z in the intersection of varieties, understand the complement of Z in the intersection; i.e., the residual set to Z. The intersection determines a class , the intersection product, in the Chow group of an ambient space and, in this situation, the problem is to understand the class, the residual class to Z: where means the part supported on Z; classically the degree of the part supported on Z is called the equivalence of Z.
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| dbo:abstract | In algebraic geometry, the problem of residual intersection asks the following: Given a subset Z in the intersection of varieties, understand the complement of Z in the intersection; i.e., the residual set to Z. The intersection determines a class , the intersection product, in the Chow group of an ambient space and, in this situation, the problem is to understand the class, the residual class to Z: where means the part supported on Z; classically the degree of the part supported on Z is called the equivalence of Z. The two principal applications are the solutions to problems in enumerative geometry (e.g., Steiner's conic problem) and the derivation of the , the formula allowing one to count or enumerate the points in a fiber even when they are . The problem of residual intersection goes back to the 19th century. The modern formulation of the problems and the solutions is due to Fulton and MacPherson. To be precise, they develop the intersection theory by a way of solving the problems of residual intersections (namely, by the use of the Segre class of a normal cone to an intersection.) A generalization to a situation where the assumption on regular embedding is weakened is due to . (en) |
| dbo:wikiPageExternalLink | https://kluedo.ub.uni-kl.de/frontdoor/deliver/index/docId/3750/file/Hiep_Dang_thesis.pdf |
| dbo:wikiPageID | 54145380 (xsd:integer) |
| dbo:wikiPageLength | 14796 (xsd:nonNegativeInteger) |
| dbo:wikiPageRevisionID | 1074177831 (xsd:integer) |
| dbo:wikiPageWikiLink | dbr:Projection_formula dbr:Projective_bundle dbr:Chow_ring dbr:Normal_cone dbr:Ergebnisse_der_Mathematik_und_ihrer_Grenzgebiete dbr:Bézout's_theorem dbr:Algebraic_geometry dbr:Intersection_theory dbr:Advances_in_Mathematics dbr:Chern_class dbc:Intersection_theory dbr:Euler_class dbr:Euler_sequence dbr:Scheme-theoretic_intersection dbr:Segre_class dbr:Veronese_surface dbr:Steiner's_conic_problem dbr:Intersection_product dbr:Springer-Verlag dbr:First_Chern_class dbr:Complete_intersection_morphism dbr:Infinitesimally_close dbr:Multiple-point_formula dbr:Self-intersection_formula |
| dbp:mathStatement | . (en) |
| dbp:name | Excess intersection formula (en) Jouanolou's key formula (en) |
| dbp:wikiPageUsesTemplate | dbt:'' dbt:' dbt:Citation_needed dbt:Cite_book dbt:Cite_journal dbt:Expand_section dbt:Harvtxt dbt:Reflist dbt:See_also dbt:Short_description dbt:Math_theorem |
| dcterms:subject | dbc:Intersection_theory |
| rdf:type | owl:Thing |
| rdfs:comment | In algebraic geometry, the problem of residual intersection asks the following: Given a subset Z in the intersection of varieties, understand the complement of Z in the intersection; i.e., the residual set to Z. The intersection determines a class , the intersection product, in the Chow group of an ambient space and, in this situation, the problem is to understand the class, the residual class to Z: where means the part supported on Z; classically the degree of the part supported on Z is called the equivalence of Z. (en) |
| rdfs:label | Residual intersection (en) |
| rdfs:seeAlso | dbr:Steiner's_conic_problem |
| owl:sameAs | wikidata:Residual intersection https://global.dbpedia.org/id/9r9ar |
| prov:wasDerivedFrom | wikipedia-en:Residual_intersection?oldid=1074177831&ns=0 |
| foaf:isPrimaryTopicOf | wikipedia-en:Residual_intersection |
| is dbo:wikiPageWikiLink of | dbr:Normal_cone dbr:Segre_class |
| is foaf:primaryTopic of | wikipedia-en:Residual_intersection |