List questions from birational-geometry

Published on 01 Jan 2020 - 14:53

98

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Why is this an automorphism of $\mathbb{P}^2$?

Published on 02 Jan 2020 - 1:02

224

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Degree $1$ birational map of $\mathbb{P}_k^n$

Published on 03 Jan 2020 - 15:56

94

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Algebraic characterization (or sufficient condition) when a (graded) local hypersurface has rational singularity

Published on 20 Jan 2020 - 10:38

261

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Small resolution of threefold with a node

Published on 25 Mar 2026 - 9:31

953

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Blowup along the fundamental locus of a rational map

Published on 26 Jan 2020 - 20:07

83

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Nonreduced quadric hypersurfaces

Published on 25 Mar 2026 - 9:22

107

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Resolution of the projection map $\text{proj}_P:\mathbb{P}^2\dashrightarrow\mathbb{P}^1$

Published on 30 Jan 2020 - 23:54

164

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How do I invert the rational map $(x,y)\mapsto \frac xy$ over the variety $C=(y^3=x^4+x^3)$?

Published on 11 Feb 2020 - 0:28

99

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A doubt in Birational Geometry OF Algebraic Varieties

Published on 12 Feb 2020 - 23:17

77

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Proof of the projection formula $(\pi^D)\cdot D'=D\cdot (\pi_D')$

Published on 16 Feb 2020 - 17:09

232

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Smoothness of general fiber of flat morphism

Published on 25 Feb 2020 - 22:48

67

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A subfield of $\mathbb{C}(x,y)$ invariant under an involution

Published on 25 Mar 2026 - 9:38

22

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Form of $u,v \in \mathbb{C}[x,y]$ satisfying $\mathbb{C}(s_1,s_2,k_1,k_2)=\mathbb{C}(u,v)$

Published on 23 Feb 2026 - 2:40

55

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The form of $w \in \mathbb{C}(x,y)$ satisfying $\beta(w)=w$, $\beta$ an involution on $\mathbb{C}[x,y]$

Published on 25 Mar 2026 - 9:39

List Question

Birational complex smooth varieties and homotopy equivalence

Why is this an automorphism of $\mathbb{P}^2$?

Degree $1$ birational map of $\mathbb{P}_k^n$

Algebraic characterization (or sufficient condition) when a (graded) local hypersurface has rational singularity

Small resolution of threefold with a node

Blowup along the fundamental locus of a rational map

Nonreduced quadric hypersurfaces

Resolution of the projection map $\text{proj}_P:\mathbb{P}^2\dashrightarrow\mathbb{P}^1$

How do I invert the rational map $(x,y)\mapsto \frac xy$ over the variety $C=(y^3=x^4+x^3)$?

A doubt in Birational Geometry OF Algebraic Varieties

Proof of the projection formula $(\pi^D)\cdot D'=D\cdot (\pi_D')$

Smoothness of general fiber of flat morphism

A subfield of $\mathbb{C}(x,y)$ invariant under an involution

Form of $u,v \in \mathbb{C}[x,y]$ satisfying $\mathbb{C}(s_1,s_2,k_1,k_2)=\mathbb{C}(u,v)$

The form of $w \in \mathbb{C}(x,y)$ satisfying $\beta(w)=w$, $\beta$ an involution on $\mathbb{C}[x,y]$

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