User Charles Staats

75 votes

17 answers

10k views

Facts from algebraic geometry that are useful to non-algebraic geometers

asked Aug 23, 2010 at 17:49

66 votes

3 answers

4k views

Reasons to prefer one large prime over another to approximate characteristic zero

asked May 16, 2013 at 0:57

60 votes

1 answer

7k views

Why "open immersion" rather than "open embedding"?

asked Dec 7, 2010 at 2:53

49 votes

2 answers

12k views

Kunneth formula for sheaf cohomology of varieties

asked Aug 5, 2010 at 19:03

49 votes

20 answers

20k views

Sources for BibTeX entries

asked Apr 6, 2010 at 21:42

45 votes

8 answers

10k views

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

asked Sep 21, 2010 at 14:51

39 votes

6 answers

9k views

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

asked Sep 30, 2010 at 15:42

39 votes

8 answers

7k views

Geometric intuition for limits

asked May 2, 2010 at 17:54

39 votes

17 answers

5k views

Slick ways to make annoying verifications

asked Jul 22, 2010 at 16:07

38 votes

5 answers

7k views

Why does so much recent work involve K3 surfaces?

asked Mar 23, 2011 at 20:33

38 votes

2 answers

4k views

A geometric characterization for arithmetic genus

asked Mar 31, 2012 at 20:21

34 votes

1 answer

18k views

Matsumura: "Commutative Algebra" versus "Commutative Ring Theory"

asked May 20, 2010 at 19:48

29 votes

1 answer

2k views

Why and how did preschemes become schemes?

asked Feb 16, 2011 at 16:26

29 votes

2 answers

1k views

Can the holomorphic image of $(\mathbb{C}^*)^n$ be open but not dense

asked May 8, 2012 at 21:36

24 votes

2 answers

4k views

Why is the degree:rank ratio of a vector bundle called its "slope"?

asked Jun 29, 2011 at 6:00

18 votes

2 answers

3k views

Is the blowup of a normal scheme necessarily normal?

asked Sep 4, 2010 at 18:38

17 votes

1 answer

4k views

A Relative Algebraic Hartogs Lemma

asked Feb 2, 2012 at 17:39

16 votes

2 answers

1k views

Is the support of a flat sheaf flat?

asked Feb 10, 2012 at 20:30

16 votes

1 answer

2k views

Why is Proj of any graded ring isomorphic to Proj of a graded ring generated in degree one?

asked Apr 2, 2010 at 4:16

16 votes

5 answers

5k views

An advanced exposition of Galois theory

asked Jul 12, 2010 at 21:49

15 votes

3 answers

2k views

A nontrivial surface on which any two curves intersect

asked Jun 16, 2010 at 0:21

15 votes

5 answers

6k views

Non-cohomological proof that the pullback of an ample bundle by a finite morphism is ample

asked Apr 26, 2011 at 2:38

14 votes

1 answer

3k views

An elementary proof that the degree of a map of spheres determines its homotopy type

asked May 21, 2010 at 20:38

11 votes

3 answers

972 views

Is Krull dimension non-increasing along ring epimorphisms?

asked Jan 16, 2011 at 0:44

11 votes

1 answer

630 views

Can flatness be specified by a natural coherent sheaf?

asked Sep 7, 2012 at 20:53

10 votes

0 answers

330 views

Smooth, complete varieties on which "zero is effective"

asked Jul 4, 2013 at 21:57

9 votes

1 answer

2k views

Why is (line bundle, appropriate rational section) not a standard kind of divisor?

asked Jan 28, 2011 at 4:22

9 votes

2 answers

685 views

What is known about the "moduli space of morphisms" $X \to Y$?

asked Nov 4, 2010 at 17:17

8 votes

2 answers

537 views

Prime avoidance in adjacent degrees

asked Feb 10, 2011 at 18:12

8 votes

2 answers

404 views

Homomorphisms from $\mathbb{R}$ to $\mathrm{Homeo}^+(\mathbb{R})$, or "fractional iterations"

asked Jul 8, 2010 at 14:28

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69 Questions

Facts from algebraic geometry that are useful to non-algebraic geometers

Reasons to prefer one large prime over another to approximate characteristic zero

Why "open immersion" rather than "open embedding"?

Kunneth formula for sheaf cohomology of varieties

Sources for BibTeX entries

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

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

Geometric intuition for limits

Slick ways to make annoying verifications

Why does so much recent work involve K3 surfaces?

A geometric characterization for arithmetic genus

Matsumura: "Commutative Algebra" versus "Commutative Ring Theory"

Why and how did preschemes become schemes?

Can the holomorphic image of $(\mathbb{C}^*)^n$ be open but not dense

Why is the degree:rank ratio of a vector bundle called its "slope"?

Is the blowup of a normal scheme necessarily normal?

A Relative Algebraic Hartogs Lemma

Is the support of a flat sheaf flat?

Why is Proj of any graded ring isomorphic to Proj of a graded ring generated in degree one?

An advanced exposition of Galois theory

A nontrivial surface on which any two curves intersect

Non-cohomological proof that the pullback of an ample bundle by a finite morphism is ample

An elementary proof that the degree of a map of spheres determines its homotopy type

Is Krull dimension non-increasing along ring epimorphisms?

Can flatness be specified by a natural coherent sheaf?

Smooth, complete varieties on which "zero is effective"

Why is (line bundle, appropriate rational section) not a standard kind of divisor?

What is known about the "moduli space of morphisms" $X \to Y$?

Prime avoidance in adjacent degrees

Homomorphisms from $\mathbb{R}$ to $\mathrm{Homeo}^+(\mathbb{R})$, or "fractional iterations"