Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 20 for “"Algebraic Varieties"”.
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Algebraic aspects of propositional logic
… the category Bool of Boolean algebras, the algebraic counterpart of classical propositional logic. We provide an algebraic definition of theories and models of classical logic and provide algebraic algorithms to determine whether a chosen formula is a theorem of a given theory of classical …
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Negative answers to some positivity questions
… 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 space at …
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Algebraic Geometry of Bayesian Networks
We develop the necessary theory in algebraic geometry to place Bayesian networks into the realm of algebraic statistics. This allows us to create an algebraic geometry--statistics dictionary. In particular, we study the algebraic varieties defined by the conditional independence statements of …
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Some Results on the Degeneracy of Entire Curves and Integral Points in the Complements of Divisors
… Theorem to the case of holomorphic curves into algebraic varieties intersecting numerically equivalent ample divisors. In chapter 4, we improve Ru's defect relation (see \cite{ru15}) and the height inequality (see \cite{ru}) in the case when $X$ is a normal projective surface and $D_j$, $1 \leq …
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Log geometry and extremal contractions
… (in short, MMP) aims at classifying projective algebraic varieties from a birational point of view. That means that starting from a projective algebraic variety X, [Delta] it is allowed to change the variety under scrutiny as long as its field of rational functions remains the same. In this …
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On the Quantum Cohomology of Fano Toric Manifolds and the Intersection Cohomology of Singular Symplectic Quotients
… decomposition theorem for singular algebraic varieties. Using this surjectivity result and the localization technique, we can relate the pairings of the intersection cohomology classes to the equivariant cohomology classes in M. We show that a theorem of Kalkman has a direct …
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Enumerative algebraic geometry via techniques of symplectic topology and analysis of local obstructions
Enumerative geometry of algebraic varieties is a fascinating field of mathematics that dates back to the nineteenth century. We introduce new computational tools into this field that are motivated by recent progress in symplectic topology and its influence on enumerative geometry. The most …
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The algebraic statistics of sampling, likelihood, and regression
This thesis is about statistical models and algebraic varieties. Algebraic Statistics unites these two concepts, turning algebraic structure into statistical insight. Featured here are three types of models that have such an algebraic structure. Linear Gaussian covariance models are continuous …
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On the geometry and topology of moduli spaces of multi-polygonal linkages
… are studied. These spaces turn out to be compact algebraic varieties. Multi-quadrilateral linkages whose moduli spaces are at most one dimensional are classified. The dimensions and some Euler characteristics are computed, and conditions under which these spaces are smooth manifolds are …
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Resolution of Stratifolds and Connection to Mather's Abstract Pre-Stratified Spaces
Many spaces which naturally occur in topology and algebraic geometry are not manifolds, but have a decomposition as a disjoint union of manifolds. Examples include algebraic varieties, orbit spaces of proper smooth group actions on manifolds and mappings cylinders of maps between manifolds. In 1998 …
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Zariski structures and simple theories
… in the case of the simple theory given by an algebraically closed field with a generic predicate. Comparing Zariski structure methods with corresponding techniques in algebraic geometry, I show the notions of etale morphism and unramified Zariski cover essentially coincide for smooth algebraic …
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Geometry of the Hitchin Morphism and Spectral Correspondences
… classes of sheaves of arbitrary rank on a given algebraic curve and twisted 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 …
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Representation theory of the global Cherednik algebra
… of Cherednik algebras associated to a complex algebraic varieties which carries the action of a finite group. First, we prove that the Knizhnik-Zamolodchikov functor from the category of P-coherent modules for the Cherednik algebra to finite dimensional modules over the Hecke algebra is …
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Geometric Theory of Parshin Residues
… residues of meromorphic top-forms on algebraic varieties. Parshin's theory is a generalization of the classical one-dimensional residue theory. The main difference between the Parshin's definition and the one-dimensional case is that in higher dimensions one computes the residue not at …
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Dualities and Categorical Structures from 2D Up
… key tools of holographic duality and categorical algebraic geometry. The use of the former is justified by the lack of a non-perturbative formulation of String Theory, whereas the latter is dictated by the great advancement there has been in the past decades in studying algebraic varieties …
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Obstructions to rational and integral points
… obstructions to rational and integral points on varieties. The first concerns the S-unit equation, which asks for solutions to x + y = 1 with x and y both S-units, or units in Z = Z[1/S]. This is equivalent to finding the set of Z-points of P1 \ {0, 1, [infinity]}. We follow work of …
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Categorifications of Cluster Varieties
… thesis we study additive categorifications of algebraic varieties whose coordinate rings admit a cluster algebra structure. The presence of a cluster structure has important implications for the geometry of a variety including the existence of canonical linearly independent sets of regular …
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Convex optimization methods for graphs and statistical modeling
… of structured models that satisfy certain algebraic constraints. The common theme underlying these approaches is the development of computational methods based on convex optimization, which are in turn useful in a broad array of problems in signal processing and machine learning. The …
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The structure of spaces of valuations and the local uniformization problem
… of singularities is a major problem in algebraic geometry. Local uniformization can be seen as its local version. For varieties over fields of characteristic zero, local uniformization was proved by Zariski in 1940 and resolution of singularities was proved by Hironaka in 1964. For …