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Derived Categories of Derived Grassmannians
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Derived Categories of Derived Grassmannians
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This paper establishes semiorthogonal decompositions for derived Grassmannians of perfect complexes with Tor-amplitude in $[0,1]$. This result verifies the author's Quot formula conjecture [J21a] and generalizes and strengthens Toda's result in [Tod23]. We give applications of this result to various classical situations such as blowups of determinantal ideals, reducible schemes, and varieties of linear series on curves. Our approach utilizes the framework of derived algebraic geometry, allowing us to work over arbitrary base spaces over $\mathbb{Q}$. It also provides concrete descriptions of Fourier-Mukai kernels in terms of derived Schur functors.
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Cited by 1 Pith paper
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Instantons on the Blown-up Surface and the Affine Vertex Algebra
Rank-r instanton cohomology on the blow-up of a surface is shown to assemble into basic representations of the affine Lie algebra gl_r, confirming the Vafa–Witten prediction.
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