List questions from projective-schemes

Published on 07 Feb 2023 - 12:45

101

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How do I define a map from points on a curve to lines through them?

Published on 13 Feb 2023 - 6:09

135

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How do I interpret the intersection of a variety with a "non-closed hyperplane?"

Published on 03 Mar 2023 - 7:22

93

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Sheaf morphism from closed subscheme is a closed immersion

Published on 07 Mar 2023 - 15:22

169

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Dimensions of cohomology of ideal sheaf

Published on 17 Mar 2023 - 11:19

45

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defining ideal of an ellipse and a curve in $\mathbb{P}^2$

Published on 27 Mar 2023 - 10:11

122

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Why are these two projective schemes isomorphic?

Published on 12 Apr 2023 - 0:27

187

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Pushforward of the Segre embedding in K-theory

Published on 25 Mar 2026 - 7:43

172

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Two definitions of scheme theoretic dual projective space

Published on 27 May 2023 - 17:48

81

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Automorphism of $k$ varieties is induced by automorphism of $\mathbb{P}_k^n$ (exercise 5.1.24 in Q Liu)

Published on 09 Jul 2023 - 8:08

44

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Sheaf cohomology free module

Published on 17 Jul 2023 - 11:48

143

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If a resolution $f:Y\to X$ satisfies $R^if_\omega_Y=0$ and $R^if_\mathcal{O}_Y=0$ for all $i>0$, then do we have $f_*\omega_Y=\omega_X$?

Published on 19 Jul 2023 - 15:21

57

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For a Fano threefold $X$, is there a lower bound for $S^3$ where $S\subseteq X$ is an irreducible surface?

Published on 31 Jul 2023 - 7:26

85

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Help understanding what is the projection in problem II.6.3 (a) Hartshorne

Published on 07 Aug 2023 - 12:20

27

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Semistability and Proj quotients

Published on 09 Aug 2023 - 23:21

List Question

Understanding morphism of schemes between projective spaces defined by homogeneous coordinates

How do I define a map from points on a curve to lines through them?

How do I interpret the intersection of a variety with a "non-closed hyperplane?"

Sheaf morphism from closed subscheme is a closed immersion

Dimensions of cohomology of ideal sheaf

defining ideal of an ellipse and a curve in $\mathbb{P}^2$

Why are these two projective schemes isomorphic?

Pushforward of the Segre embedding in K-theory

Two definitions of scheme theoretic dual projective space

Automorphism of $k$ varieties is induced by automorphism of $\mathbb{P}_k^n$ (exercise 5.1.24 in Q Liu)

Sheaf cohomology free module

If a resolution $f:Y\to X$ satisfies $R^if_\omega_Y=0$ and $R^if_\mathcal{O}_Y=0$ for all $i>0$, then do we have $f_*\omega_Y=\omega_X$?

For a Fano threefold $X$, is there a lower bound for $S^3$ where $S\subseteq X$ is an irreducible surface?

Help understanding what is the projection in problem II.6.3 (a) Hartshorne

Semistability and Proj quotients

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