Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Semiorthogonal decompositions on total spaces of tautological bundles   Let U be the tautological subbundle on the Grassmannian $\mathrm{Gr}(k, n)$.
There is a natural morphism $\mathrm{Tot}(U) \to \mathbb{A}^n$. Using it, we
give a semiorthogonal decomposition for the bounded derived category
$D^b_{\mathrm{coh}}(\mathrm{Tot}(U))$ into several exceptional objects and
several copies of $D^b_{\mathrm{coh}}(\mathbb{A}^n)$. We also prove a global
version of this result: given a vector bundle $E$ with a regular section $s$,
consider a subvariety of the relative Grassmannian $\mathrm{Gr}(k, E)$ of those
subspaces which contain the value of $s$. The derived category of this
subvariety admits a similar decomposition into copies of the base and the zero
locus of $s$. This may be viewed as a generalization of the blow-up formula of
Orlov, which is the case $k = 1$.

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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: cs
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th