Using intersection theory
From the introduction: ``The main goal of this work is to present, together with the basic concepts of intersection theory, a number of concrete examples to illustrate several aspects of the calculations and uses of intersection rings, especially in enumerative geometry. `Òur intention is to indicat...
| Autor: | |
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| Tipo de recurso: | libro |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/400782 |
| Acceso en línea: | https://hdl.handle.net/2117/400782 |
| Access Level: | acceso abierto |
| Palabra clave: | Geometry, Algebraic Geometria algèbrica Varietats (Matemàtica) Classificació AMS::14 Algebraic geometry::14C Cycles and subschemes Classificació AMS::14 Algebraic geometry::14M Special varieties Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria algebraica |
| Sumario: | From the introduction: ``The main goal of this work is to present, together with the basic concepts of intersection theory, a number of concrete examples to illustrate several aspects of the calculations and uses of intersection rings, especially in enumerative geometry. `Òur intention is to indicate the richness of geometrical thinking, in problems whose natural solution is through intersection theory, with a minumum of theoretical build-up. In so doing we hope that it will become increasingly clear that a large harvest is still conceivably to be reaped from the impressively general intersection theory that is currently available. We would also like that these notes be a bridge stretching from contemporary intersection theory to more classical styles of thinking, in particular in enumerative geometry, and also the other way around. Most of the examples were studied by many workers, both classical and modern, and so our job here is, in part, to survey results that are scattered through many sources and involving many generations.'' This monograph collects the material covered by the author in eight lectures given in Mexico in 1992, and it delivers precisely what the introduction promises. Topics include: Intersection rings; Chern classes; Projective bundles; Grassmannians; Flag varieties; Characteristic numbers; Rational equivalence on a blow-up; and Complete quadrics. The results are presented in a cogent fashion, and the examples are chosen very well. Few proofs are provided, and are more often replaced with directions to the established references on the subject. This survey can be recommended to anyone seeking some exposure to classical intersection theory, and to students looking for an engaging introduction to the subject—especially if they take it as a guided tour through the literature. Reviewer: Aluffi, Paolo |
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