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Results tagged with jets
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user 154157
3
votes
0
answers
137
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How is differentiation defined on the Green-Griffiths jet bundles?
In their original paper Green and Griffiths remark that there is a differentiation operation on their jet bundles:
$$ (-)' : \mathcal{J}_{k,m} \to \mathcal{J}_{k+1,m+1} $$
Which they define on p.47 vi …
- 3,625
7
votes
0
answers
223
views
What is the relationship between higher-order derivations (in the sense of Hasse-Schmidt) an...
Let $A$ and $B$ be $R$-algebras. A Hasse-Schmidt $m$-derivation $D : A \to B$ is a tuple $(D_0, D_1, \dots, D_m)$ of $R$-linear maps $A \to B$ satisfying the generalized Leibniz law,
$$ D_k(xy) = \sum …
- 3,625
2
votes
1
answer
152
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Splitting of higher order jet sequence
Let $X$ be a smooth variety. Because $\mathcal{O}_X$ admits a canonical connection $\mathrm{d} : \mathcal{O}_X \to \Omega_X$ the sequence,
$$ 0 \to \Omega_X \to J^1(\mathcal{O}_X) \to \mathcal{O}_X \t …
- 3,625