User Sasha

14 votes

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Two definitions of a projective morphism

answered Nov 20, 2018 at 20:37

10 votes

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Can I cancel the vector bundle $E$ in an equation $E \otimes L_1 \cong E \otimes L_2$ to conclude $L_1 \cong L_2$?

answered Nov 23, 2022 at 10:04

10 votes

Monoid as a one-object category... for monoidal categories

answered Nov 4, 2013 at 16:29

10 votes

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Unique rational normal curve through d+3 points

answered Aug 18, 2016 at 8:11

9 votes

Does closed immersion induce surjection of global section

answered Feb 4, 2014 at 19:20

8 votes

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Example of injective non-linear polynomial map from $\mathbb{C}^2\to \mathbb{C}^2$

answered Oct 5, 2022 at 12:07

8 votes

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Double dual of a subsheaf of a vector bundle

answered Oct 6, 2022 at 8:47

8 votes

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Criterion for triviality of a line bundle on a projective scheme

answered Jan 4, 2017 at 17:55

8 votes

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Hilbert Scheme of Points of Riemann Sphere

answered Jan 19, 2017 at 18:09

7 votes

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Are there holomorphic vector bundles that do not holomorphically embed in any free one?

answered Oct 15, 2022 at 19:31

7 votes

Finding an example of a degree 5 rational curve in $\mathbb{P}^3$ which is not in a quadric.

answered Mar 9 at 17:25

7 votes

Why are line bundles called principal $\mathbb G_m$-bundle?

answered Mar 31, 2021 at 7:09

7 votes

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complement of Lagrangian Grassmannian

answered May 25, 2017 at 7:27

6 votes

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What is the projective bundle over $(\Bbb P^1\times\Bbb P^1)/(\Bbb Z/2)$ which isn't $\Bbb P(\mathcal{E})$ for some vector bundle $\mathcal{E}$?

answered Feb 5, 2021 at 7:04

6 votes

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Product of two Riemann surfaces $X$ with $H^1(X,T_X)<H^2(X,\mathcal{O})$

answered Jul 28, 2020 at 20:38

6 votes

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Is an irreducible affine variety isomorphic to some affine hypersurface?

answered Apr 21, 2021 at 19:41

6 votes

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Let $X\subset\mathbb{P}^1\times\mathbb{P}^1$ be cut out by $x^2=xy^6+y^3+1$. Then what is $h^0(\omega_X)$?

answered Apr 22, 2017 at 4:39

6 votes

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Is the tensor product of a locally free sheaf with its dual always globally free?

answered Nov 6, 2018 at 10:34

6 votes

If $\omega \in \bigwedge^k\mathbb{R}^d$ is decomposable over $\mathbb C$, is it decomposable over $\mathbb R$?

answered Feb 3, 2019 at 9:24

6 votes

In triangulated category, why do we use triangles, but not exact sequences?

answered Oct 20, 2019 at 16:46

6 votes

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Self-duality of Koszul resolution

answered Nov 27, 2019 at 1:25

5 votes

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Meaning of a the notation $P(E)$, where $E$ is a sheaf.

answered Oct 18, 2021 at 12:54

5 votes

The definition of special cubic fourfolds

answered Dec 13, 2021 at 18:46

5 votes

some phenomenon regarding locally free sheaves on surface

answered Jan 25, 2022 at 9:10

5 votes

Tangent bundle of Jacobian of a curve

answered Aug 3, 2022 at 18:25

5 votes

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Generic linear projection with $\text{Codim}\ge 2$ is birational (geometric proof)

answered Jul 2, 2020 at 14:04

5 votes

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Base locus under a pull-back

answered Jul 28, 2020 at 16:04

5 votes

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Down-to-earth introduction to DG categories

answered Oct 26, 2020 at 7:46

5 votes

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Is the birational map to $\mathbb{P}^n$ of a rational manifold realized by a Kodaira map of a line bundle?

answered Aug 12 at 17:07

5 votes

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Smoothness of total spaces with nice singular fibers

answered Jan 13, 2020 at 17:00

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460 Answers

Two definitions of a projective morphism

Can I cancel the vector bundle $E$ in an equation $E \otimes L_1 \cong E \otimes L_2$ to conclude $L_1 \cong L_2$?

Monoid as a one-object category... for monoidal categories

Unique rational normal curve through d+3 points

Does closed immersion induce surjection of global section

Example of injective non-linear polynomial map from $\mathbb{C}^2\to \mathbb{C}^2$

Double dual of a subsheaf of a vector bundle

Criterion for triviality of a line bundle on a projective scheme

Hilbert Scheme of Points of Riemann Sphere

Are there holomorphic vector bundles that do not holomorphically embed in any free one?

Finding an example of a degree 5 rational curve in $\mathbb{P}^3$ which is not in a quadric.

Why are line bundles called principal $\mathbb G_m$-bundle?

complement of Lagrangian Grassmannian

What is the projective bundle over $(\Bbb P^1\times\Bbb P^1)/(\Bbb Z/2)$ which isn't $\Bbb P(\mathcal{E})$ for some vector bundle $\mathcal{E}$?

Product of two Riemann surfaces $X$ with $H^1(X,T_X)<H^2(X,\mathcal{O})$

Is an irreducible affine variety isomorphic to some affine hypersurface?

Let $X\subset\mathbb{P}^1\times\mathbb{P}^1$ be cut out by $x^2=xy^6+y^3+1$. Then what is $h^0(\omega_X)$?

Is the tensor product of a locally free sheaf with its dual always globally free?

If $\omega \in \bigwedge^k\mathbb{R}^d$ is decomposable over $\mathbb C$, is it decomposable over $\mathbb R$?

In triangulated category, why do we use triangles, but not exact sequences?

Self-duality of Koszul resolution

Meaning of a the notation $P(E)$, where $E$ is a sheaf.

The definition of special cubic fourfolds

some phenomenon regarding locally free sheaves on surface

Tangent bundle of Jacobian of a curve

Generic linear projection with $\text{Codim}\ge 2$ is birational (geometric proof)

Base locus under a pull-back

Down-to-earth introduction to DG categories

Is the birational map to $\mathbb{P}^n$ of a rational manifold realized by a Kodaira map of a line bundle?

Smoothness of total spaces with nice singular fibers