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Subcanonicity of Codimension Two Subvarieties
 

Summary: Subcanonicity of Codimension Two
Subvarieties
Enrique ARRONDO
Departamento de ´Algebra
Facultad de Ciencias Matem´aticas
Universidad Complutense de Madrid
28040 Madrid, Spain
Enrique Arrondo@mat.ucm.es
Recibido: 5 de Febrero de 2004
Aceptado: 3 de Junio de 2004
ABSTRACT
We prove that smooth subvarieties of codimension two in Grassmannians of lines
of dimension at least six are rationally numerically subcanonical. We prove the
same result for smooth quadrics of dimension at least six under some extra con-
dition. The method is quite easy, and only uses Serre's construction, Porteous
formula and Hodge index theorem.
Key words: subcanonicity, codimension two, Grassmannians, quadrics.
2000 Mathematics Subject Classification: 14M07.
Introduction
The main open problem about (complex) subvarieties of small codimension is Hart-

  

Source: Arrondo, Enrique - Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid

 

Collections: Mathematics