List questions from complex-geometry

Published on 26 Mar 2026 - 3:11

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understanding algebraic proof in complex geometry

Published on 21 Mar 2023 - 7:46

42

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prove $\frac{1}{2\pi i}dz/z$ is the generator of $H^1(\Bbb{P}^1\setminus \{0,\infty\},\Bbb{Z})$

Published on 22 Mar 2023 - 2:44

117

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Dominant morphisms between projective varieties

Published on 25 Mar 2026 - 11:52

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What is the definition of a fiber of a vector bundle in algebraic geometry?

Published on 26 Mar 2026 - 11:18

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Is $\{(z_1,z_2) \in \mathbb{C}^2 :|z_1|=|z_2| = 1, z_1^m = z_2^n\}$ a circle?

Published on 28 Mar 2023 - 22:46

65

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A special line bundle on a product $X\times Y$ is the pullback of a line bundle on the Albanese variety $\mathrm{Alb}(X\times Y)$

Published on 25 Mar 2026 - 17:21

108

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two different definition of relative differential are the same?

Published on 29 Mar 2023 - 13:50

211

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Local systems defined by higher homotopy groups

Published on 30 Mar 2023 - 5:41

153

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Can a plane with n punctures be considered a riemann surface?

Published on 29 Mar 2026 - 12:25

82

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Farkas & Kra Riemann surfaces Proposition III.5.10

Published on 29 Mar 2026 - 12:25

121

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Laplacian comparison with Lefschetz decomposition

Published on 26 Mar 2026 - 6:20

38

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Farkas & Kra Riemann surfaces theorem III.5.12

Published on 29 Mar 2026 - 12:25

26

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$f$ can only be quadratic if its Hessian determinant is constant. How about complex case

Published on 01 Apr 2023 - 10:20

74

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Understanding theorem III.8.7 in Farkas & Kra Riemann surfaces

Published on 29 Mar 2026 - 12:26

List Question

First chern class of canonical line bundle on $CP^n$

understanding algebraic proof in complex geometry

prove $\frac{1}{2\pi i}dz/z$ is the generator of $H^1(\Bbb{P}^1\setminus \{0,\infty\},\Bbb{Z})$

Dominant morphisms between projective varieties

What is the definition of a fiber of a vector bundle in algebraic geometry?

Is $\{(z_1,z_2) \in \mathbb{C}^2 :|z_1|=|z_2| = 1, z_1^m = z_2^n\}$ a circle?

A special line bundle on a product $X\times Y$ is the pullback of a line bundle on the Albanese variety $\mathrm{Alb}(X\times Y)$

two different definition of relative differential are the same?

Local systems defined by higher homotopy groups

Can a plane with n punctures be considered a riemann surface?

Farkas & Kra Riemann surfaces Proposition III.5.10

Laplacian comparison with Lefschetz decomposition

Farkas & Kra Riemann surfaces theorem III.5.12

$f$ can only be quadratic if its Hessian determinant is constant. How about complex case

Understanding theorem III.8.7 in Farkas & Kra Riemann surfaces

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