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Algebraic variety
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Mathematics
Area of mathematics
Geometry and topology
Algebraic geometry
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Words: 706
Articles: 30
An algebraic variety is a geometric space locally described by polynomial equations, together with its regular functions.
Table of contents
706
30
Smooth algebraic curve
Algebraic variety
13
Affine algebraic set
Algebraic variety
98
3
Coordinate ring
Affine algebraic set
24
Vanishing loci of ideal sums and intersections
Affine algebraic set
23
Irreducible components of two intersecting complex hyperbolas
Affine algebraic set
32
Function field of an algebraic variety
Algebraic variety
71
2
Dimension from the function field
Function field of an algebraic variety
21
Projective model of a finitely generated field
Function field of an algebraic variety
37
Morphism of algebraic varieties
Algebraic variety
119
3
Fiber of a morphism
Morphism of algebraic varieties
16
Isomorphism of algebraic varieties
Morphism of algebraic varieties
20
Finite morphism
Morphism of algebraic varieties
55
Projective space
Algebraic variety
388
17
Projective point
Projective space
18
Projective plane
Projective space
9
Projective linear transformation
Projective space
24
Projective variety
Projective space
313
13
Projective dimension theorem
Projective variety
26
Projective curve
Projective variety
7
Homogeneous coordinate ring
Projective variety
12
Product of projective varieties
Projective variety
145
5
Coordinate projection
Product of projective varieties
24
Segre embedding
Product of projective varieties
15
Smooth quadric surface
Product of projective varieties
83
2
Rulings of a smooth quadric surface
Smooth quadric surface
57
1
Disjoint curves on a smooth quadric surface
Rulings of a smooth quadric surface
17
Smooth projective curve
Projective variety
111
3
Local ring of a smooth algebraic curve
Smooth projective curve
19
Extension of a rational map from a smooth projective curve
Smooth projective curve
80
1
Failure of rational-map extension on a singular curve
Extension of a rational map from a smooth projective curve
39
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Algebraic geometry
Geometry and topology
Area of mathematics
Mathematics
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Function field of an algebraic variety
Solution
Solution
Solution
Smooth algebraic curve