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Results tagged with singularity-theory
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user 3377
Singularities in algebraic/complex/differential geometry and analysis of ODEs/PDEs. Singular spaces, vector fields, etc.
8
votes
2
answers
901
views
Gorenstein varieties: why the two definitions are equivalent?
There are two definitions of Gorenstein singularities
in the literature. Using Grothendieck's (or Serre's) duality, one
defines the "dualizing sheaf" an object $\hat K_M$ of derived category
of cohere …
- 42.9k
3
votes
Accepted
Bishop's compactness theorem and convergence of analytic subset
Convergence is taken in Hausdorff sense,
though you can define the structure of a complex variety (the Barlet space)
on the set of cycles, taking every irreducible component with positive integer mult …
- 9,237
13
votes
1
answer
642
views
Does a resolution of a rational singularity have rationally connected fibers?
A rational singularity is a singularity of a
complex variety $X$ such that for any
resolution $\pi:\; \tilde X\rightarrow X$ the
higher direct images $R^i\pi_*(O_{\tilde X})$
vanish for all $i>0$. Sup …
- 39.3k
18
votes
1
answer
810
views
Cohomology of real analytic coherent sheaves
Let $M$ be a real analytic variety
(if someone is concerned about distinction between
"real analytic spaces" and "real analytic varieties"
in real analytic geometry, let's assume that $M$
is both "va …
- 1,274
6
votes
Comparing fundamental groups of a complex orbifolds and their resolutions.
The proof of simple connectedness of a
resolution of quotient singularities is in this paper of mine
http://arxiv.org/abs/math/9903175 Theorem 4.1
(published in Asian J. Math. 4, 2000, no. 3, 553-56 …
- 9,237