Question

Reference request: unique minimal model in birational class for a complex surface of general type (which may not be smooth)?

score 157 · Answer 1 · 2026-03-25 15:40:06

157

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Reference request: unique minimal model in birational class for a complex surface of general type (which may not be smooth)?

Published on 25 Mar 2026 - 15:40

score 102 · Answer 2 · 2026-05-11 02:04:45

102

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Rational singularity of Spec, Proj and Spec of localization of a standard graded $2$-dimensional ring

Published on 11 May 2026 - 2:04

score 385 · Answer 3 · 2026-04-14 16:32:15

385

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Hartshorne Prop I.4.3 Proof

Published on 14 Apr 2026 - 16:32

score 683 · Answer 4 · 2026-04-16 02:38:34

683

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blow-ups of subvarieties $Y_1,Y_2$ are disjoint in the blow-up at the ideal $I(Y_1)+I(Y_2)$

Published on 16 Apr 2026 - 2:38

score 3.8k · Answer 5 · 2026-04-12 15:48:32

3.8k

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Understanding rational maps in Algebraic Geometry-Examples of birational equivalence between varieties

Published on 12 Apr 2026 - 15:48

score 112 · Answer 6 · 2026-04-11 17:21:03

112

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Determining singular locus from fibers of a resolution

Published on 11 Apr 2026 - 17:21

score 989 · Answer 7 · 2026-04-14 21:07:10

989

Views

Pullback of pushforward of ample divisor under birational morphism

Published on 14 Apr 2026 - 21:07

score 266 · Answer 8 · 2026-04-10 01:16:17

266

Views

Contraction morphism for surface

Published on 10 Apr 2026 - 1:16

score 441 · Answer 9 · 2026-05-10 15:29:09

441

Views

Criterion on nefness of a divisor on algebraic surfaces

Published on 10 May 2026 - 15:29

score 419 · Answer 10 · 2026-04-09 19:17:09

419

Views

Finite generated sheaf of graded $\mathcal{O}_X$ algebra

Published on 09 Apr 2026 - 19:17

score 166 · Answer 11 · 2026-04-14 07:52:17

166

Views

Birational morphisms of surfaces

Published on 14 Apr 2026 - 7:52

score 38 · Answer 12 · 2026-05-11 02:45:44

38

Views

connected components of birational real surfaces

Published on 11 May 2026 - 2:45

score 58 · Answer 13 · 2026-03-25 15:41:11

58

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Choosing a ray and order of the operations in the minimal model program

Published on 25 Mar 2026 - 15:41

score 65 · Answer 14 · 2026-03-25 15:42:33

65

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Why do we have $\overline{\operatorname{Mov}(X)}\subset \overline{\operatorname{Eff}(X)}$ for any normal variety $X$?

Published on 25 Mar 2026 - 15:42

score 118 · Answer 15 · 2026-05-10 23:54:28

118

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Dominant morphisms between projective varieties

Published on 10 May 2026 - 23:54

List Question

Reference request: unique minimal model in birational class for a complex surface of general type (which may not be smooth)?

Rational singularity of Spec, Proj and Spec of localization of a standard graded $2$-dimensional ring

Hartshorne Prop I.4.3 Proof

blow-ups of subvarieties $Y_1,Y_2$ are disjoint in the blow-up at the ideal $I(Y_1)+I(Y_2)$

Understanding rational maps in Algebraic Geometry-Examples of birational equivalence between varieties

Determining singular locus from fibers of a resolution

Pullback of pushforward of ample divisor under birational morphism

Contraction morphism for surface

Criterion on nefness of a divisor on algebraic surfaces

Finite generated sheaf of graded $\mathcal{O}_X$ algebra

Birational morphisms of surfaces

connected components of birational real surfaces

Choosing a ray and order of the operations in the minimal model program

Why do we have $\overline{\operatorname{Mov}(X)}\subset \overline{\operatorname{Eff}(X)}$ for any normal variety $X$?

Dominant morphisms between projective varieties

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