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Showing 1 to 20 of 21 for “"line bundles"”.
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On quaternionic line bundles
Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1999.
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Volumes of line bundles on schemes
The volume of a line bundle is an invariant defined in terms of a limit superior. It is a fundamental question whether this limit superior is a limit. It has been shown that this is always the case on generically reduced proper schemes over arbitrary fields. We show that volumes are limits in two …
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Line Bundles on Projective Homogeneous Spaces
… formula for the Euler character of a homogeneous line bundle on G/H generalizing Weyl's character formula. The canonical line bundle on G/H is rarely negative ample. A consequence of this is, that G/H is Frobenius split only when H is an extension of a parabolic subgroup by a Frobenius kernel of …
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Ample subschemes and partially positive line bundles
… to algebraic geometry: divisors correspond to line bundles and ample line bundles classify projective embeddings. However, subvarieties and algebraic cycles of higher codimension are regarded as much more complicated objects and not well understood in general. The first paper of the thesis …
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Equivariant line bundles with connection on the Drinfeld upper half-space Ω⁽²⁾
… of GL<sub>2</sub> by studying equivariant line bundles with connection on the Drinfeld half-plane Ω⁽¹⁾. In this thesis, we will follow the idea of Ardakov-Wadsley and extend their techniques to GL<sub>3</sub> by studying the Drinfeld upper half-space Ω⁽²⁾ of dimension 2.
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Line bundles and integrality conditions in quantum mechanics and quantum field theory
A complete theory for the line bundle structure in quantum mechanics and quantum field theory is given. This includes a general method for constructing curvature terms and flat connection terms. The necessary and sufficient condition for the existence of the integrality condition is obtained. The …
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The Frobenius direct image of line bundles and the structure of representations
… groups in positive characteristic, the induced line bundles, ${\cal L}$($\lambda$), on the flag variety G/B, are important objects of study. E.g., their global sections form representations of G which are dual to the Weyl modules. In this thesis, our central object of study is the direct image …
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Expressions for the generating function of the Donaldson invariants for CP²
… of the u-plane integral in terms of determinant line bundles. For the product of the determinant line bundles, the local and global anomalies vanish. Moreover, the product has a canonical trivialization. We show that the u-plane integral also arises as the stationary phase approximation of a …
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THE INDEX THEOREM FOR QUASI-TORI
The Index theorem for holomorphic line bundles on complex tori asserts that some cohomology groups of a line bundle vanish according to the numbers of negative and positive eigenvalues of the associated hermitian form. In this thesis, this theorem is generalized to quasi-tori, i.e. connected …
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Motivic symmetric ring spectrum representing algebraic K-theory
… and solved by introducing a category of vector bundles with strictly associative tensor product that is also strictly commutative with line bundles.
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Metric Geometry of Quiver Flag Varieties and Balanced Embeddings
… of the identity matrix. A hermitian metric on a line bundle is balanced if its Bergman kernel is identically constant. We study the relationship between balanced manifolds and balanced metrics, and generalize their correspondence to the case of weakly exceptional sequence of globally generated …
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Strange duality on elliptic and K3 surfaces
… between two spaces of global sections of natural line bundles on moduli spaces of sheaves on a fixed variety. It has been proved in full generality on curves by Marian and Oprea, and by Belkale. There have been ongoing work on the Strange Duality on surfaces by various people. In the current …
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Negative answers to some positivity questions
… of questions related to positivity properties of line bundles on algebraic varieties. The examples are based on studying the geometry of varieties that admit pseudo automorphisms of positive entropy, and in particular on the action of standard Cremona transformations on blow-ups of projective …
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Projective Geometry for Perfectoid Spaces
… analog of projective space correspond to line bundles on X together with some extra data, reflecting the classical theory. Along the way we give a complete classification of vector bundles on the perfectoid unit disk, and compute the Picard group of the perfectoid analog of projective …
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Quantum geometric Langlands correspondence in positive characteristic: the GLN case
… k \ Fp. Let BunN be the stack of rank N vector bundles on C and Ldet 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 …
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Holomorphic chains on the projective line
… on a smooth algebraic curve are tuples of vector bundles on the curve together with the homomorphisms between them. A type of a holomorphic chain is a tuple t of integers consisting of the ranks and degrees of the underlying vector bundles. The definition of holomorphic chains was introduced and …
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Geometry of the Hitchin Morphism and Spectral Correspondences
… pairs on another algebraic curve, mostly from a linear-algebraic standpoint. We aim to generalize the language of classical spectral correspondence by the annihilating polynomials of pairs. In a particular application, we realize a generic elliptic curve as a spectral cover of the complex …
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Equivariant Modules
… We use our technique to show that each Mλ has a linear resolution and describe also the resolution of its truncations. In Chapter 3 we look at a family of equivariant complexes. One can find this family in the appendix of the famous book by D. Eisenbud "Commutative Algebra with a View Towards …
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Much ado about nothing: The superconformal index and Hilbert series of three dimensional N =4 vacua
… the descriptions of the Hilbert series of a line bundle on the ADHM quiver variety via localisation, and via Hanany’s monopole formula. Finally, we study the action of the Poisson algebra of the coordinate ring on the Hilbert series of line bundles. We restrict to the case of looking at the …
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Gromov-Witten theory in dimensions two and three
… mathematics. The first object is the class of P2-bundles over a smooth curve C of genus g. Our bundles are of the form P(L0 + L1 +L2) for arbitrary line bundles L0, L1 and L2 over C. We compute the partition functions of these invariants for all classes of the form s + nf, where s is a section, f …
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