As discussed briefly in Section Aside: Types of Schemes, there are a number of different increasingly specialised data types for schemes. It is often useful to check whether a given scheme can be thought of as belonging to one of these more specialised classes, and if so then actually making the type change. In this section we document a number of such type-change intrinsics, most of which are of the form IsSpecialisedType. These intrinsics always return a boolean value. If that value is true then they typically also return a new scheme of the given specialised type, although in some trivial cases this does not happen. Of course, each of the different types of scheme has its own methods of construction independently of these intrinsics.
Returns true if and only if X is an affine space.
Returns true if and only if X is a projective space. Projective space here includes the case of scrolls.
Returns true if and only if X is a projective space in the usual sense: its coordinate ring has a single grading in which all the variables have weight one.
Returns true if and only if X is a zero-dimensional scheme (but not the empty scheme). See Section Zero-dimensional Schemes for intrinsics which apply to clusters.
Returns true if and only if X is a one-dimensional scheme which arises as the scheme defined by a single equation in a two-dimensional ambient space. See Chapter PLANE ALGEBRAIC CURVES for intrinsics which apply to curves.
Returns true if and only if X is a curve (in the sense of IsCurve(X)) which is nonsingular and defined by an equation of degree 2. See Chapter RATIONAL CURVES AND CONICS for intrinsics which apply to such conics.
Returns true if and only if X is a curve (in the sense of IsCurve(X)) which has genus 0. See Chapter RATIONAL CURVES AND CONICS for intrinsics which apply to rational curves.[Next][Prev] [Right] [Left] [Up] [Index] [Root]