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Shrugs
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7 votes
1 answer
383 views

History of Serre Duality and its topological/geometric analogue.

5 votes
4 answers
636 views

For any $A\in M_n(\mathbb{R})$, there is a $B$ s.t. $\operatorname{rank}(A)+\operatorname{rank}(B)=n$ and $AB=0$.

4 votes
1 answer
200 views

Hartshorne IV.3.9 To prove a Lemma of Bertini regarding degree $d$ curves in $\mathbb{P}^3$.

4 votes
0 answers
76 views

Hartshorne Exercise V.5.5 Every geometrically ruled surface over a fixed curve $C$ is birationally equivalent

4 votes
0 answers
47 views

What are the advantages to viewing Hermitian symmetric domains as a moduli for Hodge structures?

3 votes
0 answers
89 views

When does an algebraic group have $PSL_2$ as a quotient?

3 votes
1 answer
230 views

Hartshorne Algebraic Geometry Exercise III.11.5 (On Picard groups of Formal Completions)

3 votes
1 answer
408 views

Grothendieck Group of a Nonsingular Curve (Hartshorne Exercise II.6.11).

3 votes
1 answer
90 views

Dimension of space of linear transformations commuting with some matrix.

3 votes
0 answers
117 views

Simple modules over a matrix ring and their the dimension of their tensor product over the base field.

3 votes
1 answer
617 views

Hartshorne Exercise II.6.1 Proving that $\operatorname{Cl}(X\times\mathbb{P}^n)\cong \operatorname{Cl}(X)\times \mathbb{Z}$.

3 votes
0 answers
400 views

What does linear equivalence geometrically mean for varieties?

3 votes
0 answers
134 views

What should/can be learnt in a reading course on Elliptic Curves?

3 votes
1 answer
75 views

Cohomological implications of Twisting by Effective Nef Divisors

2 votes
1 answer
326 views

Hartshorne Exercise II.6.10 Proving existence of a filtration for coherent sheaves supported on a closed subscheme.

2 votes
1 answer
110 views

Singular homology of a quotient of $\mathbb{C}P^n$ by an order $2$ action.

2 votes
1 answer
139 views

An Incorrect Solution to Hartshorne Ex. III.5.5(c).

2 votes
1 answer
69 views

A category theoretic claim in Mumford's Lectures on Curves on an Algebraic Surface.

1 vote
1 answer
244 views

Why is the etale fundamental group of $\mathbb{P}^n$ trivial?

1 vote
0 answers
53 views

Explanation of a particular example in Mumford's Lectures on Curves on an Algebraic Surface

1 vote
0 answers
42 views

The linear system associated to a blow-up(of surfaces)

1 vote
1 answer
72 views

Locally free sheaves on flat site versus Zariski site

1 vote
1 answer
46 views

Why should analytic classes sit inside $H^{p,p}(X)$ for various values of $p>0$?

1 vote
0 answers
37 views

Why does this curve over $\mathbb{R}$ have no odd degree line bundles?

1 vote
1 answer
156 views

Applications of the Lefschetz Hyperplane Theoren

1 vote
1 answer
286 views

$\mathbb{P}^n$-bundles over a regular noetherian scheme Hartshorne Exercise II.7.10(b).

1 vote
1 answer
75 views

Examples for when the quotient ring is necessarily / not necessarily an extension of the residue field.

1 vote
0 answers
162 views

Computing the blow-up of $\mathbb{P}^2$ at $p_0=[1:1:1]$ and then at $p=[1:0:0]$.

1 vote
1 answer
376 views

Hartshorne Exercise II.7.7(c) Studying a particular blow-up and ruled surface.

1 vote
0 answers
101 views

If $\mathscr{C}$ is the sheaf continuous real-valued functions on $X$, then when is $H^1(X,\mathscr{C})=0$?