Definition of Subschemes. Meaning of Subschemes. Synonyms of Subschemes

- 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...
- 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})}...
- 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...
- 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...
- as a finite union of locally closed subschemes i Y : Y → X {\displaystyle i_{Y}:Y\to X} such that for each subscheme Y {\displaystyle Y} of the covering...
- \ \{{\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...
- universal property of the fiber product of schemes. If X and Z are closed subschemes of a scheme Y, then the fiber product X ×Y Z is exactly the intersection...
- 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...
- of vertex operators on the cohomology of the Hilbert schemes of finite subschemes of a complex algebraic surface, and (in joint work with Fishel and Teleman)...
- 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...