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Showing 1 to 9 of 9 for “"Derived categories"”.
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Derived categories of coherent sheaves on rational homogeneous manifolds
… in $D^b(Coh\,\mathbb{P}^n)$, the bounded derived category of coherent sheaves on $\mathbb{P}^n$. In a series of papers M. M. Kapranov generalized this result to flag manifolds of type $A_n$ and quadrics. In another direction, Y. Kawamata has recently proven existence of complete …
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On Fourier-Mukai type functors
In this thesis we study functors between bounded derived categories of sheaves and how they can be expressed in a geometric way, namely whether they are isomorphic to a Fourier-Mukai transform. Specifically, we describe the behavior of a functor between derived categories of smooth projective …
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Limits of stability conditions and their geometry
After giving a brief survey of the study of derived categories in algebraic geometry, I present a pair of research papers. The first, joint with Daniel Halpern-Leistner and Jeffrey Jiang, introduces the notion of quasi-convergent paths in the space of stability conditions. We prove that …
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Quantum geometric Langlands correspondence in positive characteristic: the GLN case
… the line bundle on BunN given by determinant of derived global sections. In this thesis, we construct an equivalence of derived categories of modules for certain localizations of the twisted crystalline differential operator algebras DBunNet and DBunN, L-1/cdet The first step of the argument is …
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Making art to make identity : shifting perceptions of self amongst historically disadvantaged South African artists
… between concepts of 'freedom' and externally-derived categories of value within socio-economic limitations in a transforming South African art world is also explored. I also show how artworks act as sites of transcultural encounter for artists, within their awareness of different gazes and …
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Pursuing the meaning of expressiveness: a holistic, radical contextualist account of lexical expressives
… and (iii) functional role. The empirically derived categories of lexical expressives obtained in the new typology are then used to investigate their contribution to meaning in discourse through a questionnaire-based study. The results reveal, firstly, that lexical expressives can contribute …
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Investigating Aerosol Composition with Low Cost Optical Particle Counters
… belongs to. This method is run for both compound-derived categories which mimic real PM sources (Sea Salt, Biomass Burning, Dust, and Urban Smog), and property-derived aerosols which present more idealized conditions. The results of this method are near-perfect classification for single mode …
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Human concept cognition and semantic relations in the unified medical language system: A coherence analysis.
… (49 participants) sorted 60 food names into categories followed by simultaneous description of the derived categories to explain the rationale for category judgment. The second group (40 participants) performed sorting 47 semantic relations (the nonhierarchical associative types) into 5 …
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Towards studying of the higher rank theory of stable pairs
… theory coming from the moduli of objects in the derived category of $X$. This yields the first deformation-theoretic construction of a higher-rank enumerative theory for Calabi-Yau threefolds. We calculate this enumerative theory for local $\mathbb{P}^1$ using the Graber-Pandharipande virtual …