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Showing 1 to 7 of 7 for “"projective line"”.
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Holomorphic chains on the projective line
… rational vector parameter corresponds to a given linearization of the GIT quotient. R^n is partitioned into locally closed subsets called chambers where the stability does not change. The moduli spaces in each chamber do not change. The case in which the underlying bundles are all line bundles is …
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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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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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Equivariant quantum connections in positive characteristic
… in the example of the cotangent bundle of the projective line, and explore the relationship with Varchenko's construction of mod p solutions to the quantum differential equation. We then prove the compatibility of the equivariant quantum Steenrod operations with the quantum differential and …
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L-functions of twisted elliptic curves over function fields
… and its twists over the function field of the projective line over a finite field. This method requires computing the number of points on an elliptic curve over a finite field, for which we present a novel algorithm. If the j-invariant of an elliptic curve over a function field is non-constant, …
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MOTIVIC HOCHSCHILD HOMOLOGY
… such as the multiplicative group scheme or the projective line. To do so, we tackle the problem from the more general perspective of left tensored ∞-categories. The construction of the extended action moreover allows us to prove that in the event R= R ∧ R is an idempotent E_∞ motivic ring …
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Pairs of geometric foliations of regular and singular surfaces
… curves (called harmonic mean curvature lines in \cite{garciasotomayorharmonic}). The asymptotic curves exist in hyperbolic regions of surfaces and have been well studied. The characteristic curves are in certain ways the analogy of the asymptotic curves in elliptic regions. In this …