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Mathematics Subject Classification: 14D20, 14J60; Secondary 14D22, 14F06, 13D02
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Revista de Matemática Teoría y Aplicaciones
Print version ISSN 1409-2433
Rev. Mat vol.30 n.1 San José Jan./Jun. 2023
http://dx.doi.org/10.15517/rmta.v30i1.50518
Artículo
Codimension 1 distributions on three dimensional hypersurfaces
Distribuciones de codimensión 1 en hipersuperficies tridimensionales
1Universidad Estatal de Campinas, Departamento de Matematica, Campinas, Brasil; jardim@ime.unicamp.br
2Instituto Federal de Sergipe, Coordinación de Agropecuaria, Sergipe, Brasil; danilo.santiago@ifs.edu.br
We show that codimension 1 distributions with at most isolated singularities on threefold hypersurfaces Xd ⊂ P4 of degree d provide interesting examples of stable rank 2 reflexive sheaves. When d ≤ 5, these sheaves can be regarded as smooth points within an irreducible component of the moduli space of stable reflexive sheaves. Our second goal goes in the reverse direction: we start from a well-known family of stable locally free sheaves and provide examples of codimension 1 distributions of local complete intersection type on Xd.
Keywords: holomorphic distributions; stable sheaves; moduli spaces; isolated singularities.
Mostramos que las distribuciones de codimensión 1 con a lo mas singularidades aisladas en hipersuperficies Xd ⊂ P4 de dimensión 3 y grado d proporcionan ejemplos interesantes de haces reflexivos estables de rango 2. Cuando d ≤ 5, estos haces se pueden considerar como puntos suaves dentro de una componente irreducible del espacio de moduli de los haces reflexivos estables. Nuestro segundo objetivo va en dirección inversa: partimos de una familia conocida de haces estables localmente libres y proporcionamos ejemplos de distribuciones de codimensión 1 del tipo intersección completa local en Xd.
Palabras clave: distribuciones holomorfas; haces estables; espacios de moduli; singularidades aisladas.
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Received: April 01, 2022; Revised: August 17, 2022; Accepted: October 18, 2022
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