118 Gaussian prime spirals 2012-03-16T22:26:08.793

83 Why is the Hodge Conjecture so important? 2011-02-03T14:21:11.857

67 Is there a complex surface into which every Riemann surface embeds? 2015-10-27T16:05:45.623

66 Is there a complex structure on the 6-sphere? 2009-10-22T23:16:31.963

65 Complex structure on $S^6$ gets published in Journ. Math. Phys 2015-06-24T22:20:24.527

60 Does $\Bbb{CP}^{2n} \# \Bbb{CP}^{2n}$ ever support an almost complex structure? 2015-09-02T20:03:16.353

52 Simplest examples of nonisomorphic complex algebraic varieties with isomorphic analytifications 2011-06-21T18:46:09.033

46 What do Weierstrass points look like? 2009-12-17T21:57:25.473

42 Atiyah's paper on complex structures on $S^6$ 2016-10-31T20:01:46.353

41 Which nonlinear PDEs are of interest to algebraic geometers and why? 2011-05-26T11:44:02.877

36 Algebraic Geometry versus Complex Geometry 2009-11-12T03:34:53.627

36 Do compact complex manifolds fall into countably many families? 2017-05-01T22:18:47.553

33 What's the difference between a real manifold and a smooth variety? 2010-05-08T02:52:54.523

33 A geometric characterization for arithmetic genus 2012-03-31T20:21:46.697

33 Complex manifold with subvarieties but no submanifolds 2016-05-02T14:46:19.843

31 A paper to the question, if the six dimensional sphere is a complex manifold 2011-01-02T09:10:17.147

31 Example of a compact Kähler manifold with non-finitely generated canonical ring? 2012-02-08T00:14:34.183

30 The Relationship between Complex and Algebraic Geomety 2009-11-10T17:31:27.740

30 "The complex version of Nash's theorem is not true" 2011-03-27T16:55:21.737

30 Is S^2 x S^4 a complex manifold? 2012-02-28T21:03:42.263

30 The error in Petrovski and Landis' proof of the 16th Hilbert problem 2014-06-17T02:05:30.510

28 Can the holomorphic image of $(\mathbb{C}^*)^n$ be open but not dense 2012-05-08T21:36:54.690

28 What are the higher homotopy groups of a K3 suface? 2014-11-03T19:27:02.263

28 What is the current understanding regarding complex structures on the 6-sphere? 2017-02-28T03:20:35.817

27 Two definitions of Calabi-Yau manifolds 2010-02-11T16:35:54.773

27 Is there a geometric realization of $\mathbf{C}((t))$-varieties? 2016-12-25T02:01:34.710

25 Intuition for Primitive Cohomology 2010-02-08T17:56:35.670

25 Which almost complex manifolds admit a complex structure? 2011-01-23T14:37:31.420

24 Complex vector bundles that are not holomorphic 2009-11-30T19:00:59.417

24 Which Kahler Manifolds are also Einstein Manifolds? 2011-03-07T13:53:01.230

24 de Rham vs Dolbeault Cohomology 2012-04-27T16:14:03.167

24 Rep Theory Consequences of Bott--Weil--Borel 2013-02-06T16:18:48.213

24 Biholomophic non-Algebraically Isomorphic Varieties 2013-05-27T22:33:16.237

23 Roadmap for Mirror Symmetry 2010-09-26T23:11:52.677

23 Diffeomorphic Kähler manifolds with different Hodge numbers 2010-10-19T06:44:02.383

23 Complex manifolds in which the exponential map is holomorphic 2011-06-16T00:53:11.733

23 Non-compact complex surfaces which are not Kähler 2012-02-20T05:12:37.463

23 Is there any holomorphic version of the tubular neighborhood theorem? 2012-11-25T11:50:43.627

22 Do hyperKahler manifolds live in quaternionic-Kahler families? 2010-01-27T21:11:27.623

22 Why do people think that abelian varieties are the hardest case for the Hodge conjecture? 2010-03-03T22:36:37.627

22 Kähler structure on cotangent bundle? 2010-06-02T02:15:27.300

22 References for "modern" proof of Newlander-Nirenberg Theorem 2010-06-17T15:13:31.010

22 Accumulation of algebraic subvarieties: Near one subvariety there are many others (?) 2011-05-28T15:31:39.680

21 Hsiung on the Complex Structure of $S^6$ 2012-07-10T20:30:30.023

21 function field analogy and global/absolute geometry 2014-07-22T19:55:08.977

20 Stein Manifolds and Affine Varieties 2009-10-23T12:54:09.320

20 GAGA and Chern classes 2010-03-31T18:55:36.507

20 Almost Complex Structure approach to Deformation of Compact Complex Manifolds 2012-06-18T15:56:57.990

19 Is Hodge theory somehow connected with a Galois group action Gal(C/R)? 2009-11-04T14:00:20.230

19 Holomorphic vector fields acting on Dolbeault cohomology 2010-03-24T16:34:55.347

19 Projective embedding of symplectic manifolds 2011-03-27T15:52:08.837

19 Rational or elliptic curves on Calabi-Yau threefolds 2011-07-07T12:50:44.793

19 Weitzenböck Identities 2012-09-14T12:07:44.507

19 Must an algebraic variety with trivial tangent bundle be an abelian variety? 2015-04-20T22:08:56.220

18 Almost complex 4-manifolds with a "holomorphic" vector field 2009-12-22T00:14:00.767

18 Exercises in Hodge Theory 2010-02-15T14:05:07.500

18 Are the eigenvalues of the Laplacian of a generic Kähler metric simple? 2010-07-21T15:52:36.247

18 Examples of compact complex non-Kähler manifolds which satisfy $h^{p,q} = h^{q,p}$ 2014-11-03T23:18:51.997

18 If a variety $X$ has finite automorphism group, is the same true for its $n$-fold self-products? 2018-02-21T10:34:40.673

17 Deformations of Kähler manifolds where Hodge decomposition fails? 2010-10-19T16:40:11.650

17 Theorem of Bryant in higher dimensions 2011-11-20T17:48:19.700

17 Does equality of Laplacians imply Kähler? 2012-06-24T16:27:15.907

17 Moishezon manifolds with vanishing first Chern class 2012-07-28T01:52:08.050

17 Three-dimensional compact Kähler manifolds 2013-07-08T06:34:30.680

17 History of the connection between Riemann surfaces and complex algebraic curves 2014-07-23T11:26:14.977

17 Classification of complex structures on $\mathbb{R}^{2n}$ 2015-04-20T13:41:47.200

17 Tate twists and cohomology of $\mathbf{P}^1$ 2017-11-30T05:24:51.540

16 What was Weierstrass's counterexample to the Dirichlet Principle? 2010-10-14T16:59:19.153

16 Projective variety with no syzygies but not isomorphic to projective space 2010-11-06T09:00:19.270

16 When can you reverse the orientation of a complex manifold and still get a complex manifold? 2010-11-30T21:41:31.683

16 Accumulation of algebraic subvarieties: Near one subvariety there are many others (?), 3 2011-10-11T22:01:29.123

16 Is there an integrable complex structure on $\mathrm{SU}(3)$? 2015-10-06T18:50:34.387

16 Relationship between the signs of different notions of curvature in complex geometry 2017-12-11T16:42:15.077

15 Representations of surface groups via holomorphic connections 2009-12-15T17:30:43.590

15 Compact holomorphic symplectic manifolds: what's the state of the art? 2011-09-15T12:31:09.867

15 Geometric meaning of L-genus 2012-03-01T18:13:43.230

15 Vector bundles on vector bundles 2014-03-04T11:00:59.503

15 What is the holomorphic sectional curvature? 2014-03-21T14:38:29.040

15 Can all $L^2$ holomorphic functions on a domain vanish at a particular point? 2014-11-21T00:11:57.320

15 Can Calabi-Yau manifolds have nonabelian discrete symmetry groups? 2015-12-10T01:01:17.590

15 What is a Futaki invariant, what is the intuition behind it, and why is it important? 2016-02-13T16:05:56.237

15 The Order of Approximation of a Rational Map 2016-09-07T10:03:32.877

15 Finiteness aspects of Deligne cohomology 2017-11-28T22:58:48.277

15 Do $\mathbb{A}^1-S$ and $\mathbb{A}^1-\{0,1\}$ have a finite etale cover in common? 2018-01-05T17:59:47.557

15 Holomorphic line bundles on $\mathbb{P}^1$ from gluing data 2018-03-02T02:23:47.193

14 Algebraic de Rham cohomology vs. analytic de Rham cohomology 2010-03-12T03:25:57.283

14 Picard Groups of Moduli Problems 2010-05-20T04:43:20.173

14 Griffiths and Harris reference 2010-12-10T23:52:57.227

14 Surfaces containing curves of arbitrarily negative self-intersection 2011-05-05T11:57:02.703

14 When is a Form a Kähler Form? 2011-08-20T20:57:47.083

14 flatness in complex analytic geometry 2011-09-13T14:42:11.930

14 Can there exist Chow motives/motivic cohomology for compact Kähler manifolds? 2012-11-03T08:57:44.437

14 Why are the holomorphic line bundle sections finite dimensional? 2013-01-27T16:15:59.847

14 Are all holomorphic vector bundles on a contractible complex manifold trivial? 2014-05-05T13:21:01.873

14 List of Applications of the $\partial\overline{\partial}$-lemma 2016-05-25T12:13:18.570

14 Are $\partial$-exact and $\bar\partial$-exact forms also $\partial\bar\partial$-exact? 2017-02-06T23:32:32.590

14 Gromov's quick "proof" of Lefchetz Hyperplane Theorem 2017-06-27T22:40:11.563

14 Do prime ideals in polynomial ring generate prime ideals in the ring of holomorphic functions? 2017-11-21T12:35:08.267

14 p-adic Poincaré Lemma 2017-11-30T12:12:31.253