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Words: 3k
Articles: 117
Table of contents
3k
117
Algebraic variety
Algebraic geometry
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
Irreducible topological space
Algebraic geometry
84
2
Irreducible component
Irreducible topological space
20
Noetherian Zariski topology
Irreducible topological space
40
Zariski-closed set
Algebraic geometry
22
Zariski-open set
Algebraic geometry
37
1
Distinguished open set
Zariski-open set
19
Hilbert Nullstellensatz
Algebraic geometry
165
3
Projective Nullstellensatz
Hilbert Nullstellensatz
74
1
Irrelevant ideal of projective space
Projective Nullstellensatz
30
Quasi-compactness of an affine variety
Hilbert Nullstellensatz
45
Zariski density of the complex exponential graph
Algebraic geometry
36
Degree of a projective curve
Algebraic geometry
213
7
Bézout theorem
Degree of a projective curve
60
2
Projective plane curve
Bézout theorem
16
Intersection multiplicity
Bézout theorem
17
Hilbert polynomial
Degree of a projective curve
33
Generic hyperplane section of a projective curve
Degree of a projective curve
28
Degree under a linear projective embedding
Degree of a projective curve
30
Embedding dependence of projective degree
Degree of a projective curve
32
Twisted cubic
Algebraic geometry
89
2
Nondegenerate projective variety
Twisted cubic
17
Degree obstruction to the twisted cubic being a complete intersection
Twisted cubic
44
Genus distinguishes equal-degree projective curves
Algebraic geometry
31
Zariski tangent space
Algebraic geometry
314
8
Dimension from minimum tangent dimension
Zariski tangent space
29
Smooth locus of a variety
Zariski tangent space
156
3
Singular point of an algebraic variety
Smooth locus of a variety
32
Density of the smooth locus
Smooth locus of a variety
94
1
Jacobian criterion
Density of the smooth locus
43
Singular locus of a product with a smooth variety
Zariski tangent space
17
Tangent spaces of a product of two nodal line pairs
Zariski tangent space
37
Tangent-space obstruction between two unions of three lines
Zariski tangent space
51
Krull dimension of an affine variety
Algebraic geometry
40
Affine hypersurface
Algebraic geometry
141
3
Tangent hyperplane section
Affine hypersurface
36
Singular points of an irreducible affine plane cubic
Affine hypersurface
59
Singular cylinder over a nodal curve
Affine hypersurface
21
Projective hypersurface
Algebraic geometry
290
7
Affine cone
Projective hypersurface
31
Pencil of plane curves
Projective hypersurface
103
2
Fermat cubic curve
Pencil of plane curves
25
Cubic pencil with a triangular member
Pencil of plane curves
38
Affine cone over a projective hypersurface
Projective hypersurface
44
Projective quadric cone with one singular vertex
Projective hypersurface
97
1
Projective variety with a prescribed-dimensional singular locus
Projective quadric cone with one singular vertex
62
Determinantal variety
Algebraic geometry
92
2
Smooth projective surface from overlapping rank-one coordinates
Determinantal variety
51
Rank-one determinantal variety
Determinantal variety
26
Birational variety
Algebraic geometry
50
1
Blowup of the affine plane at the origin
Birational variety
39
Normalization of an algebraic curve
Algebraic geometry
112
4
Geometric genus
Normalization of an algebraic curve
35
1
Genus one curve
Geometric genus
20
Normalization of a nodal curve
Normalization of an algebraic curve
55
1
Normalization of y squared equals x times x minus one squared
Normalization of a nodal curve
35
Divisor on an algebraic curve
Algebraic geometry
432
14
Degree of a divisor
Divisor on an algebraic curve
16
Linear equivalence of divisors
Divisor on an algebraic curve
39
Principal divisor on an algebraic curve
Divisor on an algebraic curve
130
2
Divisor class on the projective line
Principal divisor on an algebraic curve
50
Principal divisor with one simple zero and one simple pole
Principal divisor on an algebraic curve
45
Complete linear system of a divisor
Divisor on an algebraic curve
82
2
Very ample divisor
Complete linear system of a divisor
55
1
High-degree divisor is very ample on a smooth projective curve
Very ample divisor
38
Riemann-Roch theorem
Divisor on an algebraic curve
145
5
Canonical divisor
Riemann-Roch theorem
129
4
Canonical divisor of the projective line
Canonical divisor
44
Genus of a smooth plane curve
Canonical divisor
26
1
Smooth plane quartic
Genus of a smooth plane curve
16
Canonical map
Canonical divisor
35
Gonality
Algebraic geometry
22
Hyperelliptic curve
Algebraic geometry
165
4
Even-degree hyperelliptic model
Hyperelliptic curve
134
3
Compactification of y squared equals x to the eighth minus one
Even-degree hyperelliptic model
48
Canonical divisor of an even-degree hyperelliptic curve
Even-degree hyperelliptic model
64
1
Canonical map of a hyperelliptic curve
Canonical divisor of an even-degree hyperelliptic curve
28
Rational map of projective varieties
Algebraic geometry
57
2
Indeterminacy locus
Rational map of projective varieties
15
Projective Cremona transformation
Rational map of projective varieties
21
Nonsingular plane cubic
Algebraic geometry
19
Plane curve
Algebraic geometry
63
2
Canonical map of a smooth plane curve
Plane curve
29
Semicubical parabola
Plane curve
13
Ramification divisor
Algebraic geometry
21
Product surface without low-genus curves
Algebraic geometry
50
Projection of a plane curve from an exterior point
Algebraic geometry
34
Ancestors
(4)
Geometry and topology
Area of mathematics
Mathematics
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