User Donu Arapura - MathOverflow

86 votes

Accepted

Introductory book on spectral sequences

answered Apr 22, 2010 at 18:36

83 votes

Accepted

Vanishing cycles in a nutshell?

answered Feb 20, 2011 at 19:14

58 votes

Ways to prove the fundamental theorem of algebra

answered May 17, 2010 at 11:01

44 votes

Why are local systems and representations of the fundamental group equivalent

answered Mar 11, 2010 at 1:41

43 votes

How has modern algebraic geometry affected other areas of math?

answered Oct 5, 2011 at 9:26

35 votes

What does the Lefschetz principle (in algebraic geometry) mean exactly?

answered Mar 8, 2012 at 18:57

35 votes

Proving Hodge decomposition without using the theory of elliptic operators?

answered Jun 17, 2010 at 18:19

33 votes

What is the Zariski topology good/bad for?

answered Apr 16, 2010 at 12:37

33 votes

How to explain to an engineer what algebraic geometry is?

answered Oct 23, 2018 at 10:25

32 votes

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What is the inverse image sheaf necessary for in algebraic geometry?

answered Sep 30, 2010 at 16:23

32 votes

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Non-compact complex surfaces which are not Kähler

answered Feb 20, 2012 at 14:30

32 votes

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Gabber's original proof of his purity theorem

answered Feb 16, 2016 at 11:28

31 votes

A down-to-earth introduction to the uses of derived categories

answered Sep 22, 2010 at 12:19

29 votes

Motivating the de Rham theorem

answered Oct 27, 2010 at 15:56

29 votes

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A nice explanation of what is a smooth (l-adic) sheaf?

answered Jul 20, 2010 at 23:57

29 votes

What is the difference between homology and cohomology?

answered Apr 10, 2010 at 18:59

26 votes

de Rham vs Dolbeault Cohomology

answered Apr 28, 2012 at 12:08

25 votes

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Computing fundamental groups and singular cohomology of projective varieties

answered Feb 21, 2010 at 14:59

25 votes

Accepted

Why should an algebraic geometer care about singular / simplicial (co)homology?

answered Jul 12, 2021 at 12:12

25 votes

Why does representing functors help solving Diophantine equations?

answered May 9, 2022 at 15:05

24 votes

Accepted

Why are Stein manifolds/spaces the analog of affine varieties/schemes in algebraic geometry?

answered May 22, 2019 at 17:08

24 votes

equivalence of Grothendieck-style versus Cech-style sheaf cohomology

answered Mar 18, 2010 at 22:26

24 votes

Work of ICM 2010 plenary speakers (and other humans)

answered Aug 6, 2010 at 14:41

24 votes

Extending vector bundles on a given open subscheme, reprise

answered Aug 17, 2010 at 14:37

24 votes

Work of plenary speakers at ICM 2014

answered Oct 18, 2013 at 18:54

24 votes

Quillen's motivation of higher algebraic K-theory

answered Mar 31, 2014 at 20:36

24 votes

Fundamental groups of compact Kähler manifolds

answered May 17, 2017 at 15:15

23 votes

What does the Jacobian of a curve tell us about the curve?

answered Aug 11, 2013 at 1:57

23 votes

Accepted

On polarized (pure) Hodge structures

answered Oct 13, 2010 at 11:29

23 votes

What mistakes did the Italian algebraic geometers actually make?

answered Mar 26, 2010 at 13:59

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409 Answers

Introductory book on spectral sequences

Vanishing cycles in a nutshell?

Ways to prove the fundamental theorem of algebra

Why are local systems and representations of the fundamental group equivalent

How has modern algebraic geometry affected other areas of math?

What does the Lefschetz principle (in algebraic geometry) mean exactly?

Proving Hodge decomposition without using the theory of elliptic operators?

What is the Zariski topology good/bad for?

How to explain to an engineer what algebraic geometry is?

What is the inverse image sheaf necessary for in algebraic geometry?

Non-compact complex surfaces which are not Kähler

Gabber's original proof of his purity theorem

A down-to-earth introduction to the uses of derived categories

Motivating the de Rham theorem

A nice explanation of what is a smooth (l-adic) sheaf?

What is the difference between homology and cohomology?

de Rham vs Dolbeault Cohomology

Computing fundamental groups and singular cohomology of projective varieties

Why should an algebraic geometer care about singular / simplicial (co)homology?

Why does representing functors help solving Diophantine equations?

Why are Stein manifolds/spaces the analog of affine varieties/schemes in algebraic geometry?

equivalence of Grothendieck-style versus Cech-style sheaf cohomology

Work of ICM 2010 plenary speakers (and other humans)

Extending vector bundles on a given open subscheme, reprise

Work of plenary speakers at ICM 2014

Quillen's motivation of higher algebraic K-theory

Fundamental groups of compact Kähler manifolds

What does the Jacobian of a curve tell us about the curve?

On polarized (pure) Hodge structures

What mistakes did the Italian algebraic geometers actually make?