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Results tagged with complex-geometry
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user 29657
Complex geometry is the study of complex manifolds, complex algebraic varieties, complex analytic spaces, and, by extension, of almost complex structures. It is a part of differential geometry, algebraic geometry and analytic geometry.
4
votes
1
answer
960
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Do there exist double points on an algebraic surface in $\mathbb{P}_{\mathbb{C}}^3$ that are...
The title explains it all.
I'm familiar with the du val singularities on surfaces, also known as rational double points. In http://homepages.warwick.ac.uk/~masda/surf/more/DuVal.pdf, 2.1, they are ch …
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3
votes
1
answer
176
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What can a quartic surface in $\mathbb{P}^3$ with an ordinary quadruple point look like?
All varieties will be projective and over $\mathbb{C}$.
If $S$ is any surface in $\mathbb{P}^3$ of degree 2 that posseses an ordinary double point, it follows easily that $S$ is projectively isomorph …
- 469
3
votes
1
answer
361
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Reference for the classification of (singular) degree 4 surfaces in $\mathbb{P}^3_{\mathbb{C...
I was told singular quartic algebraic surfaces in $\mathbb{P}^3_{\mathbb{C}}$ have been completely classified and their singularities have been described.
Can anyone provide me with a resource where t …
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0
votes
2
answers
256
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Another reference request about dualizing sheaves for nodal surfaces
My advisor told me the following:
Let $\Sigma$ be a singular surface over $\mathbb{C}$ whose singularities are all ordinary quadratic, or more generally Duval singularities. Let $\epsilon: S \rightar …
- 469
4
votes
1
answer
856
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Reference for fact about dualizing sheaf of singular varieties
Today i was talking with my advisor and she told me the following fact:
Let $S$ be a singular surface in $\mathbb{P}^3_{\mathbb{C}}$ of degree $d$. Writing $\omega_\Sigma$ for the dualizing sheaf and …
- 469
4
votes
3
answers
1k
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Divisor class group on blowup of nodal surface
The following got no answer on mathstackexchange. I believe it not to be hard, but maybe it is a little specialized?
All varieties will be over $\mathbb{C}$ and projective unless stated otherwise.
I …
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0
votes
0
answers
645
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Quicker way to show that the restriction to a open subvariety is again proper?
Dear all,
Let $f: X \rightarrow Y$ be a morphism of projective varieties over $\mathbb{C}$. Also let $V \subset Y$ be a nontrivial open subvariety and set $U:= f^{-1}(V)$.
I would like to show that …
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