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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

7 votes
0 answers
566 views

How can you spot the blow-up of $\mathbb P^3$ at a set of points not in general position?

In a previous question, it appears that a collection of points in $\mathbb P^2$ is in general position precisely when the blow-up of $\mathbb P^2$ at those points has no $(-2)$-curve. Is there a simil …
SAG1's user avatar
  • 325
3 votes
0 answers
102 views

Hilbert scheme of curves in weighted projective spaces

I am trying to learn about Hilbert scheme of curves in a weighted protective space. In my next step I am interested in Hilbert scheme of curves in a complete intersection in a weighted protective sp …
SAG1's user avatar
  • 325
4 votes
1 answer
275 views

QQ-Gorenstein smoothing of a surface and a finite group action

Let S be a singular complex algebraic surface. Let $\psi: \chi \rightarrow \Delta$ be a QQ-Gorenstein smoothing of S (central fibre is isomorphic to S). Let G be a finite group acting on the fibres of …
SAG1's user avatar
  • 325
8 votes
1 answer
447 views

Computing H^2(X, T_X(-\log D))

Let $X\subset \mathbb P^3$ be a smooth variety and $D \subset X$ be an effective, reduced, irreducible divisor. My question is the following. If I know the defining equations of $X$ and $D$ then is t …
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  • 325