User Carlos Esparza

37 votes

1 answer

1k views

If $A$, $B$ are abelian groups such that $\mathrm{Hom}(A, G) \cong \mathrm{Hom}(B, G)$ for all abelian groups $G$, must $A$ and $B$ be isomorphic?

asked Jun 16, 2020 at 21:17

11 votes

3 answers

1k views

Is every smooth projective variety contained in a chain of smooth projective varieties of increasing dimension?

asked Aug 10, 2022 at 8:04

11 votes

2 answers

846 views

Is it possible to obtain the inequality $\|\nabla f\|_{L^{2p}} \leq C (\|f\|_{L^\infty} \|f\|_{W^{2, p}})^{1/2}$ from interpolation/harmonic analysis?

asked Jan 6, 2023 at 22:31

10 votes

0 answers

273 views

Looking for counterexamples: Are maximal tori in the automorphism groups of smooth complex quasiprojective varieties conjugate?

asked Feb 19 at 22:42

7 votes

2 answers

619 views

Does Peetre's theorem hold in complex analysis?

asked Nov 9, 2019 at 18:25

6 votes

1 answer

582 views

Equivalent definitions of Kodaira dimension

asked Feb 24, 2022 at 0:00

6 votes

0 answers

322 views

What's the point of fine sheaves? (As opposed to soft ones)

asked May 27, 2022 at 15:08

5 votes

1 answer

442 views

Is the determinant line bundle of a coherent sheaf functorial (between sheaves of the same rank)?

asked Oct 4, 2022 at 16:55

5 votes

0 answers

138 views

Are open subsets of a $\sigma$-compact LCH space $\mathcal{K}$-analytic?

asked Sep 10, 2021 at 7:21

4 votes

0 answers

101 views

Serre vanishing on one-point blow-ups

asked Aug 20, 2020 at 16:29

4 votes

2 answers

769 views

smooth functions on closed intervals with values in infinite-dimensional spaces

asked Nov 12, 2020 at 3:17

3 votes

1 answer

266 views

If subharmonic functions converge weakly to a subharmonic limit, why do their smoothings converge uniformly on compact sets?

asked Nov 18, 2020 at 6:50

3 votes

0 answers

134 views

Restriction of complete 1-forms to closed submanifolds (Sharpe's book on Cartan geometries)

asked Dec 29, 2020 at 1:11

3 votes

0 answers

91 views

Can you find a Darboux basis for any skew integral form on a full-rank lattice in $ℂ^n$ so that the first $n$ vectors are $ℂ$-linearly independent?

asked Feb 6, 2023 at 3:48

3 votes

1 answer

1k views

Friedrichs mollifiers and Sobolev spaces

asked Feb 13, 2021 at 0:16

2 votes

1 answer

388 views

Are "transverse" hyperplane sections of nondegenerate irreducible projectice varieties always nondegenerate

asked Nov 13, 2021 at 23:57

2 votes

0 answers

730 views

What algebraic condition corresponds to injectivity of a morphism of varieties?

asked Dec 8, 2021 at 9:41

1 vote

0 answers

159 views

Sobolev interpolation inequality for relatively compact subdomains

asked Jan 12, 2022 at 0:06

1 vote

0 answers

41 views

Deriving the general interior elliptic estimate from the compactly supported case

asked Feb 18, 2022 at 9:49

1 vote

1 answer

447 views

A distribution $u$ such that all of its derivatives are of order zero is smooth

asked Jan 18, 2021 at 0:56

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20 Questions

If $A$, $B$ are abelian groups such that $\mathrm{Hom}(A, G) \cong \mathrm{Hom}(B, G)$ for all abelian groups $G$, must $A$ and $B$ be isomorphic?

Is every smooth projective variety contained in a chain of smooth projective varieties of increasing dimension?

Is it possible to obtain the inequality $\|\nabla f\|_{L^{2p}} \leq C (\|f\|_{L^\infty} \|f\|_{W^{2, p}})^{1/2}$ from interpolation/harmonic analysis?

Looking for counterexamples: Are maximal tori in the automorphism groups of smooth complex quasiprojective varieties conjugate?

Does Peetre's theorem hold in complex analysis?

Equivalent definitions of Kodaira dimension

What's the point of fine sheaves? (As opposed to soft ones)

Is the determinant line bundle of a coherent sheaf functorial (between sheaves of the same rank)?

Are open subsets of a $\sigma$-compact LCH space $\mathcal{K}$-analytic?

Serre vanishing on one-point blow-ups

smooth functions on closed intervals with values in infinite-dimensional spaces

If subharmonic functions converge weakly to a subharmonic limit, why do their smoothings converge uniformly on compact sets?

Restriction of complete 1-forms to closed submanifolds (Sharpe's book on Cartan geometries)

Can you find a Darboux basis for any skew integral form on a full-rank lattice in $ℂ^n$ so that the first $n$ vectors are $ℂ$-linearly independent?

Friedrichs mollifiers and Sobolev spaces

Are "transverse" hyperplane sections of nondegenerate irreducible projectice varieties always nondegenerate

What algebraic condition corresponds to injectivity of a morphism of varieties?

Sobolev interpolation inequality for relatively compact subdomains

Deriving the general interior elliptic estimate from the compactly supported case

A distribution $u$ such that all of its derivatives are of order zero is smooth