- to the set of
closed subschemes of P n × S {\displaystyle \mathbb {P} ^{n}\times S} that are flat over S. The
closed subschemes of P n × S {\displaystyle...
-
spaces is open (closed, respectively), i.e. if open
subschemes of Y are
mapped to open
subschemes of X (and
similarly for closed). For example, finitely...
- \ \{{\text{closed
subschemes of }}X\times _{k}T{\text{ flat over }}T,{\text{ with
Hilbert polynomial }}P.\}} The
closed subscheme of X × H X P {\displaystyle...
-
closed subschemes of
degree 2 in a
smooth complex variety Y. Such a
subscheme consists of
either two
distinct complex points of Y, or else a
subscheme isomorphic...
-
compact open
subscheme (e.g., open
affine subscheme)
under f is compact. It is not
enough that Y
admits a
covering by
compact open
subschemes whose pre-images...
- is of
finite type if Y {\displaystyle Y} has a
covering by
affine open
subschemes V i = Spec ( A i ) {\displaystyle V_{i}=\operatorname {Spec} (A_{i})}...
-
deformations of Y in X;
there is a
natural bijection between the set of
closed subschemes of Y ×k D, flat over the ring D of dual
numbers and
having X as the special...
-
importance of
ideal sheaves lies
mainly in the
correspondence between closed subschemes and quasi-coherent
ideal sheaves.
Consider a
scheme X and a quasi-coherent...
-
integral subschemes of X are in one-to-one
correspondence with the scheme-theoretic
points of X
under the map that, in one direction,
takes each
subscheme to...
- in
scheme theory,
where a quasi-projective
scheme is a
locally closed subscheme of some
projective space. An
affine space is a Zariski-open
subset of...
