All Questions
1,159 questions
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How do I find the algebra representing the projective bundle of a direct sum of line bundles over a projective space?
I am trying to learn how to compute the projective bundle $\mathbb{P}(\mathcal{O}(a_1)\oplus \cdots \mathcal{O}(a_k))$ over some projective space using relative proj. How can I find a presentation for ...
- 1,716
-1
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1
answer
422
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on flat morphisms
Let $j:U\rightarrow X$ an open immersion between k-schemes of finite type and $f:X\rightarrow S$ a surjective k-morphism of finite type.
We suppose that $f\circ j:U\rightarrow S$ is faithfully flat, ...
- 3,472
-1
votes
1
answer
205
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Connections on vector bundles over elliptic curves - concrete computations
This is linked to my question on math.Stackexchange for which I had no answer.
I have found nowhere a historical account on connections (or rather called logarithmic connections?) that would help me ...
- 339
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1
answer
324
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property of rational functions on projective curves
I have a couple of question about the proof of Lemma 1.20.5 from Janos Kolloar's Lecture on Resolution of Singularities (page 19):
Lemma 1.20.5 Let $C$ be a reduced, irreducible projective curve (=1D ...
- 6,006
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votes
1
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895
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Restriction of a Cartier divisor
Let $X$ be a surface (so $2$-dimensional proper $k$-scheme)
$D \subset X$ an effective Cartier divisor of $X$ which corresponding to an invertible sheaf $\mathcal{L}=O_X(D)$ and
$C \subset X$ a closed ...
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-2
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1
answer
901
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One-dimensional scheme with no closed points
Can someone give a reasonably explicit example of an irreducible one-dimensional scheme with no closed points?
user137767
-2
votes
1
answer
255
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Schemes over $K_s$ and over $\bar{K}$
Let $K$ be a field. Let $X$ be a scheme over $K$. We denote by $K_s$ and by $\bar{K}$ the separable closure and the algebraic closure of $K$ respectively.
By base change we have the schemes $X_{K_s}$ ...
- 147
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1
answer
274
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The scheme $y^n = x^{2n}$ for $n$ a rational number [closed]
Let $n\geq 1$ be an integer. If $A$ is a ring, then the spectrum of $A[x,y]/(y^n - x^{2n})$ is a well-defined (affine) scheme, say $X_n$. This scheme describes the "variety" given by the equation $y^...
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1
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628
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Strongly abnormal schemes
Call a scheme $Y$ proper positive-dimensional over $\mathrm{Spec}\,\mathbb{C}$ abnormal if there exists an irreducible scheme $X$ affine of finite type over $\mathrm{Spec}\,\mathbb{C}$ and a $\mathbb{...
user141356