Question

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

score 156 · Answer 1 · 2020-07-01 15:41:43

156

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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 01 Jul 2020 - 15:41

score 100 · Answer 2 · 2020-07-21 22:17:21

100

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

Published on 21 Jul 2020 - 22:17

score 382 · Answer 3 · 2016-07-20 18:34:58

382

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Hartshorne Prop I.4.3 Proof

Published on 20 Jul 2016 - 18:34

score 680 · Answer 4 · 2016-08-26 15:18:33

680

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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 26 Aug 2016 - 15:18

score 3.8k · Answer 5 · 2016-09-04 00:01:46

3.8k

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

Published on 04 Sep 2016 - 0:01

score 109 · Answer 6 · 2016-09-17 21:00:26

109

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Determining singular locus from fibers of a resolution

Published on 17 Sep 2016 - 21:00

score 986 · Answer 7 · 2016-10-20 00:55:39

986

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Pullback of pushforward of ample divisor under birational morphism

Published on 20 Oct 2016 - 0:55

score 263 · Answer 8 · 2016-10-28 02:15:55

263

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Contraction morphism for surface

Published on 28 Oct 2016 - 2:15

score 440 · Answer 9 · 2026-03-25 05:09:45

440

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Criterion on nefness of a divisor on algebraic surfaces

Published on 25 Mar 2026 - 5:09

score 416 · Answer 10 · 2016-11-30 20:15:59

416

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

Published on 30 Nov 2016 - 20:15

score 164 · Answer 11 · 2026-03-25 04:38:12

164

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Birational morphisms of surfaces

Published on 25 Mar 2026 - 4:38

score 37 · Answer 12 · 2026-03-25 06:02:00

37

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connected components of birational real surfaces

Published on 25 Mar 2026 - 6:02

score 57 · Answer 13 · 2023-03-03 09:30:05

57

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

Published on 03 Mar 2023 - 9:30

score 64 · Answer 14 · 2023-03-06 19:02:27

64

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

Published on 06 Mar 2023 - 19:02

score 117 · Answer 15 · 2026-03-25 11:52:59

117

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Dominant morphisms between projective varieties

Published on 25 Mar 2026 - 11:52

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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