Small codimension subvarieties in homogeneous spaces
نویسندگان
چکیده
منابع مشابه
Small codimension smooth subvarieties in even-dimensional homogeneous spaces with Picard group Z
We investigate a method proposed by E. Arrondo and J. Caravantes to study the Picard group of a smooth lowcodimension subvariety X in a variety Y when Y is homogeneous. We prove that this method is strongly related to the signature σY of the Poincaré pairing on the middle cohomology of Y . We give under some topological assumptions a bound on the rank of Picard group Pic(X) in terms of σY and r...
متن کاملSubcanonicity of Codimension Two Subvarieties
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 condition. The method is quite easy, and only uses Serre’s construction, Porteous formula and Hodge index theorem.
متن کاملOrdinary Subvarieties of Codimension One
In this paper we extend the properties of ordinary points of curves [10] to ordinary closed points of one-dimensional affine reduced schemes and then to ordinary subvarieties of codimension one.
متن کاملOn Codimension Two Subvarieties in Hypersurfaces
We show that for a smooth hypersurface X ⊂ P of degree at least 2, there exist arithmetically Cohen-Macaulay (ACM) codimension two subvarieties Y ⊂ X which are not an intersection X ∩ S for a codimension two subvariety S ⊂ P. We also show there exist Y ⊂ X as above for which the normal bundle sequence for the inclusion Y ⊂ X ⊂ P does not split. Dedicated to Spencer Bloch
متن کاملOn the Picard Group of Low-codimension Subvarieties
Abstract. We introduce a method to determine if n-dimensional smooth subvarieties of an ambient space of dimension at most 2n − 2 inherit the Picard group from the ambient space (as it happens when the ambient space is a projective space, according to results of Barth and Larsen). As an application, we give an affirmative answer (up to some mild natural numerical conditions) when the ambient sp...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Indagationes Mathematicae
سال: 2009
ISSN: 0019-3577
DOI: 10.1016/s0019-3577(09)80026-8