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Results tagged with projective-resolution
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user 4428
10
votes
Free Resolution of this determinantal variety.
The standard way to construct a resolution is the following. Let $X = A^9$ and let $E$ be a 3-dim (trivial) vector bundle on $X$ such that $M \in End(E)$. Consider the relative Grassmannian $p:Gr(2,E) …
- 39.3k
5
votes
Accepted
Explicit locally free resolution of a perfect complex $E\oplus F\to (E\oplus F)\otimes \math...
Projections to the second summands define a morphism from that complex to the complex
$$
F \stackrel{s}\to F(D)\tag{*}
$$
of locally free sheaves. The cone of this morphism is the complex
$$
0 \to E \ …
- 39.3k
3
votes
Vector bundles admitting resolution by ample line bundles
This holds true for projective spaces. Indeed, if $E$ is any vector bundle (even any coherent sheaf), the Beilinson spectral sequence for $E(n)$ with $n \gg 0$ gives the required resolution for $E(n)$ …
- 39.3k