All Questions
7 questions
4
votes
2
answers
434
views
Question about surface singularities
Throughout, $X$ will be a projective surface. I am looking for examples of the following surface singularities,
I) A rational singularity that is not quotient. Obviously, it has to be non-Gorenstein, ...
- 345
3
votes
1
answer
373
views
Minimal resolution of singularities of surfaces
Let $X$ be a normal projective irreducible surface over an algebraically closed field $k$. Let $\pi\colon Y\to X$ be a birational morphism, such that $Y$ is a smooth projective surface, and assume ...
- 7,722
1
vote
0
answers
125
views
Resolution of rational surfaces
Let $S$ be a rational singular complete algebraic surface over $\mathbb{C}$. Let $\phi:\tilde{S}\to S$ be a resolution of singularities with minimal possible Picard rank (i.e. minimal $\mathrm{dim}(...
- 4,189
1
vote
1
answer
247
views
Infinitesimal deformation of strict transform
Let $X$ be an affine, complex surface with isolated singularities and $\pi:\widetilde{X} \to X$ be a resolution of singularities (not necessarily minimal) i.e., $\widetilde{X}$ is non-singular and $\...
- 2,126
6
votes
1
answer
640
views
Resolution of Gorenstein rational singularities on a surface
I am reading Artin's notes "Lipman's Proof of Resolution of Singularities for Surfaces" from the book "Arithmetic Geometry". I am very confused by the proof of Lemma $6.5.$ (I am formulating it below ...
- 2,923
2
votes
1
answer
386
views
Surfaces singular along a curve
Let $C\subset\mathbb{P}^3$ be a smooth curve a degree $d$ and genus $g$. Let $\mathcal{S}$ be the system of surfaces of degree $k$ in $\mathbb{P}^3$ containing $C$ with multiplicity $\beta$.
What is ...
user47036
4
votes
1
answer
399
views
Blowing up rational singularities
Let $X$ be a projective surface embedded into $\mathbb{P}^n_{\mathbb{C}}$ having at most rational singularities. Let $\tilde{X} \to X$ be the minimal resolution of $X$. Is it possible to embed $\tilde{...
- 1,981