User Misha Verbitsky

184 votes

Widely accepted mathematical results that were later shown to be wrong?

answered Aug 18, 2010 at 19:35

25 votes

Accepted

Two definitions of Calabi-Yau manifolds

answered Feb 11, 2010 at 23:25

20 votes

Accepted

Which almost complex manifolds admit a complex structure?

answered Feb 2, 2011 at 13:24

19 votes

Accepted

Three-dimensional compact Kähler manifolds

answered Jul 15, 2013 at 12:52

14 votes

Accepted

Canonical Metric on Grassmann Manifold

answered Aug 15, 2014 at 2:54

13 votes

Accepted

Action of automorphisms of a $K3$ surface on its $(-2)$-curves

answered Oct 31, 2013 at 13:49

12 votes

Accepted

Is the deformation limit of Ricci-flat Kahler manifolds Kahler?

answered Mar 3, 2011 at 17:51

12 votes

Accepted

Deformations of Kähler manifolds where Hodge decomposition fails?

answered Oct 19, 2010 at 19:38

11 votes

Weitzenböck Identities

answered Aug 4, 2014 at 3:13

10 votes

Accepted

Infinite dimensional Riemannian geometry

answered Apr 2, 2014 at 14:28

10 votes

How restrictive is having zero Chern numbers for a compact complex manifold ? Same for negative Chern number?

answered Jun 29, 2022 at 15:09

9 votes

Accepted

Different occurences of the word 'period' in algebraic geometry

answered Dec 23, 2021 at 12:13

9 votes

Roadmap to learning about Ricci Flow?

answered Aug 10, 2014 at 2:18

8 votes

Accepted

What is the moduli of an algebraic torus

answered Nov 16, 2013 at 18:48

8 votes

moduli spaces are kahler?

answered Oct 28, 2013 at 15:27

8 votes

Hodge dual of de Rham cohomology and singular cohomology

answered Dec 7, 2021 at 18:59

8 votes

Accepted

Proper family deformation retracts onto special fiber

answered Apr 7, 2017 at 14:39

8 votes

Coincide between Chern-connection and Levi-Civita connection

answered Jul 25, 2022 at 21:29

8 votes

Accepted

Does it make sense to define a holomorphic structure on $\mathbb{C}P^\infty$ and vector bundles over it?

answered Oct 13, 2022 at 6:26

7 votes

Complex manifolds whose tangent and cotangent bundles are isomorphic as complex vector bundles

answered Nov 23, 2022 at 21:43

7 votes

Accepted

"Simple" Kahler manifolds

answered Feb 23, 2011 at 21:02

7 votes

Accepted

Existence of closed manifolds with more than 3 linearly independent complex structures?

answered Mar 9, 2011 at 8:27

7 votes

Accepted

Is the generic deformation of a symplectic variety affine?

answered Dec 12, 2010 at 19:26

7 votes

Accepted

Finiteness of De Rham cohomology of smooth quasi-projective varieties

answered Jan 28, 2014 at 21:55

7 votes

Is the group of isometries of a homogeneous Riemannian manifold maximal?

answered Jun 25, 2014 at 7:37

6 votes

Accepted

Ideals in the I-adic completion of a ring

answered Jun 25, 2014 at 8:46

6 votes

Accepted

The de Rham complex of a quaternion-Kahler manifold

answered Feb 1, 2014 at 15:22

6 votes

Accepted

All Kähler metrics on a complex manifold?

answered Aug 14, 2014 at 2:10

6 votes

First chern class of fibers of compact Kaehler algebraic variety

answered Aug 20, 2014 at 1:46

6 votes

Non projective hyperbolic compact complex space

answered Jul 8, 2014 at 22:51

Stack Exchange Network

108 Answers

Widely accepted mathematical results that were later shown to be wrong?

Two definitions of Calabi-Yau manifolds

Which almost complex manifolds admit a complex structure?

Three-dimensional compact Kähler manifolds

Canonical Metric on Grassmann Manifold

Action of automorphisms of a $K3$ surface on its $(-2)$-curves

Is the deformation limit of Ricci-flat Kahler manifolds Kahler?

Deformations of Kähler manifolds where Hodge decomposition fails?

Weitzenböck Identities

Infinite dimensional Riemannian geometry

How restrictive is having zero Chern numbers for a compact complex manifold ? Same for negative Chern number?

Different occurences of the word 'period' in algebraic geometry

Roadmap to learning about Ricci Flow?

What is the moduli of an algebraic torus

moduli spaces are kahler?

Hodge dual of de Rham cohomology and singular cohomology

Proper family deformation retracts onto special fiber

Coincide between Chern-connection and Levi-Civita connection

Does it make sense to define a holomorphic structure on $\mathbb{C}P^\infty$ and vector bundles over it?

Complex manifolds whose tangent and cotangent bundles are isomorphic as complex vector bundles

"Simple" Kahler manifolds

Existence of closed manifolds with more than 3 linearly independent complex structures?

Is the generic deformation of a symplectic variety affine?

Finiteness of De Rham cohomology of smooth quasi-projective varieties

Is the group of isometries of a homogeneous Riemannian manifold maximal?

Ideals in the I-adic completion of a ring

The de Rham complex of a quaternion-Kahler manifold

All Kähler metrics on a complex manifold?

First chern class of fibers of compact Kaehler algebraic variety

Non projective hyperbolic compact complex space