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4
votes
2answers
280 views

affinization of T^*CP^n

Is there an elementary description of the affinization of the algebraic cotangent bundle of $CP^n$? I know that it can be described as some sort coadjoint orbits, but I am interested in a translation ...
1
vote
0answers
117 views

compatible resolutions of singularities

Let $U$ and $V$ be complex vector spaces with an action of a finite group $G$. Denote by $P_{G,d}$ the space of $G$-equivariant polynomial maps $U\longrightarrow V$ with degree less than or equal to ...
4
votes
1answer
339 views

Hodge numbers of a Calabi-Yau 3-fold via deformation theory

In their paper "Calabi-Yau 3-folds and Moduli of Abelian Surfaces I", Gross and Popescu calculate the hodge numbers of smooth CY 3-folds obtained in the following way (see Remark 4.11 of their paper): ...
1
vote
2answers
246 views

Line bundles and rational singularities

Hi, I have some problem to understand the proof of lemma 3.2 of this article: http://www.ams.org/journals/jams/2001-14-03/S0894-0347-01-00368-X/. The lemma states the following: Let $X$ be a variety ...
5
votes
2answers
294 views

Crepant resolutions of ODP's on a 3-fold

It seems to be a well-known fact that if we have a 3-fold $X$ with only ODP singularities (ordinary double point) and a smooth Weil divisor $E$ passing through them, then by blowing-up $X$ along $E$ ...
3
votes
1answer
301 views

$A_{\infty}$ singularity

What kind of singularity is commonly meant by $A_{\infty}$?
5
votes
2answers
646 views

Do fixed point sets in equivariant crepant resolutions have the same cohomology? How about for the specific case of Nakajima quiver varieties?

A crepant resolution $f:Y\to X$ is a resolution of singularities with $f^*(K_X)=K_Y$. Crepant resolutions do not always exist, and when they exist they may not be unique. However, different crepant ...
4
votes
0answers
202 views

Embedding of a smooth variety into a complete smooth variety.

Consider the following fact from algebraic geometry: Any (complex) smooth algebraic variety can be embedded into a complete smooth variety as a locally closed set. I know how to prove this fact ...
2
votes
2answers
172 views

commuting the resolution of 1-dim singular locus and 0-dim singularities in a non isolated singularity of a surface

Let $X$ be a surface with a non isolated singularity $C = Sing(X)$ such that the curve $C$ has singularities itself. We can solve $Sing(X)$ by blowing up close points and by normalizing. Indeed, we ...
1
vote
1answer
243 views

'Reference' request: Program to work with cyclic quotient singularities.

I'm looking for program code to deal with cyclic quotient singularities on normal surfaces. In particular, at the moment I need that given a singularity $p$ like $p=\frac{1}{n}(1,a)$ the code ...
7
votes
2answers
379 views

Resolution of singularities for flat families.

Is there a resolution of singularities for flat families? More precisely, if $X \rightarrow \mathbb{A} ^n$ is a flat map, does there exist a map $Y \rightarrow X$ such that, for every $p \in ...
4
votes
1answer
288 views

Property of singularity

Let $X$ be an algebraic variety, $S \subset X$ its singular locus, and $x \in S$. Say that $x$ is good if for any neighborhood $U$ of $x$, any top differential form $\omega$ on $U \setminus S$ and ...
4
votes
2answers
548 views

Vanishing associated to a resolution of singularities

Let $\pi: V\to W$ be a resolution of singularities, let $E \subset V$ be the exceptional divisor, and let $F$ be a coherent sheaf such that $R^i\pi_*F=0$ for $i>0$. Can we conclude that ...
12
votes
0answers
326 views

When are the fibers of a resolution of singularities reduced?

I apologize if this is too much of a fishing expedition, but I've had bad luck searching for any literature on this subject, and I was hoping someone could tell me if it's too easy to be worth ...