Classification of smooth congruences of low degree
We give a complete classification of smooth congruences - i.e. surfaces in the Grassmann variety of lines in P 3C identified with a smooth quadric in P5- of degree at most 8, by studying which surfaces of P5can lie in a smooth quadric and proving their existence. We present their ideal sheaf as a qu...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 1989 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/57185 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/57185 |
| Access Level: | acceso abierto |
| Palabra clave: | 512.7 Smooth congruences surfaces in the Grassmann variety of lines cohomology postulation linear normality Hilbert scheme Geometria algebraica 1201.01 Geometría Algebraica |
| Sumario: | We give a complete classification of smooth congruences - i.e. surfaces in the Grassmann variety of lines in P 3C identified with a smooth quadric in P5- of degree at most 8, by studying which surfaces of P5can lie in a smooth quadric and proving their existence. We present their ideal sheaf as a quotient of natural bundles in the Grassmannian, what provides a perfect knowledge of its cohomology (for example postulation or linear normality), as well as many information on the Hilbert scheme of these families, such as dimension, smoothness, unirationality - and thus irreducibility - and in some cases rationality. |
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