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Results tagged with singularity-theory
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user 9871
Singularities in algebraic/complex/differential geometry and analysis of ODEs/PDEs. Singular spaces, vector fields, etc.
6
votes
1
answer
1k
views
Blowing-up an ordinary double point, then contracting the exceptional locus to a curve
Let $X\subset\mathbb P^4$ a projective hypersurface with an ordinary double point at $o\in X$.
Blow-up $\mathbb P^4$ at $o$ and let $E\simeq\mathbb P^3$ the exceptional divisor of this blow-up. Consi …
- 7,902
28
votes
Accepted
construct the elliptic fibration of elliptic k3 surface
Let $S$ be a smooth projective $K3$ surface, say over the complex numbers, and suppose that $S$ admits a (non-constant) fibration $\pi\colon S\to C$ over a curve $C$.
By the universal property of th …
- 7,902
32
votes
Accepted
Elementary short exact sequence of sheaves
Expanding the comment of Donu Arapura, let $X$ be a variety and $Y\subset X$ a subvariety.
Then, you have a short exact sequence of sheaves
$$
0\to\mathcal I_Y\to\mathcal O_X\to\mathcal O_X/\mathcal I …
- 7,902