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 36 for “"projective plane"”.
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Classifcation of Conics in the Tropical Projective Plane
This paper defines tropical projective space, TP^n, and the tropical general linear group TPGL(n). After discussing some simple examples of tropical polynomials and their hypersurfaces, a strategy is given for finding all conics in the tropical projective plane. The classification of conics and an …
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Simple and complete K-points in a modular projective plane
Thesis (M.A.)--University of Kansas, Mathematics, 1918. ; Includes bibliographical references.
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On motivic Donaldson-Thomas invariants on the local projective plane
… various moduli spaces associated to the local projective plane (ωP2). In the first project, we give a construction of an orientation data for the stack of coherent sheaves on ωP2. In the second project, we construct a d-critical locus structure on Hilbn(ωP2), which is useful for recovering the …
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Complete Tropical Bezout's Theorem and Intersection Theory in the Tropical Projective Plane
… theorem which is applicable to all tropical projective plane curves. There is a version of tropical Bezout's theorem presented in other works which applies in special cases, but we provide a proof of the theorem for all tropical projective plane curves. We provide several different …
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Floer cohomology in the mirror of the projective plane and a binodal cubic curve
… in the Landau-Ginzburg mirror to the projective plane equipped with a binodal cubic curve as anticanonical divisor. These objects correspond under mirror symmetry to the powers of the twisting sheaf 0(1), and hence their Floer cohomology groups form an algebra isomorphic to the …
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Geometric Invariant Theory Quotient of the Hilbert Scheme of Six Points on the Projective Plane
… the Hilbert scheme of six points on the complex projective plane, and provide a description of its geometric invariant theory (GIT) quotient.
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On Nonassociative Division Rings and Projective Planes
… paper. Semifields have intimate ties to finite projective planes. In short, a finite projective plane with certain restrictions gives rise to a semifield, and, in turn, a finite semifield can be used via a coordinate construction, to build a special finite projective plane. It is also shown that …
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Coloring of Metric Spaces and L(2,1)-Labeling of Graphs
… Delta2 - Delta for the incidence graph G of the projective plane PG (2, q). To prove this result, we convert the problem to a problem of packing of bipartite graphs into a complete bipartite graph. We also bound lambda(G) when G is the Kneser graph K(2k + 1, k).
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Abstract hyperovals, partial geometries, and transitive hyperovals
A hyperoval is a (q+2)- arc of a projective plane π, of order q with q even. Let G denote the collineation group of π containing a hyperoval Ω. We say that Ω is transitive if for any pair of points x, y is an element of Ω, there exists a g is an element of G fixing Ω setwise such that xg = y. …
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On planar rational cuspidal curves
… thesis studies rational curves in the complex projective plane that are homeomorphic to their normalizations. We derive some combinatorial constraints on such curves from a result of Borodzik-Livingston in Heegaard-Floer homology. Using these constraints and other tools from algebraic geometry, …
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Three-dimensional manifolds
… are proved. The most important theorem is the Projective Plane Theorem (6.1), in which it is proved that elements of the second homotopy group of a 3-manifold can be represented, in a certain sense, by 2-spheres or projective planes in the manifold. The Projective Plane Theorem is, perhaps, an …
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Number-theoretic properties of the binomial distribution with applications in arithmetic geometry
… distribution of the number of points on a smooth projective plane curve of degree d over a finite field of order q is approximated by a particular binomial distribution. We generalize their arguments to obtain a similar theorem concerning hypersurfaces in projective m-space. We briefly describe …
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Computing the Zeta Function of Two Classes of Singular Curves
… had smooth representations in either affine or projective space.In this thesis, two non-smooth situations are introduced: the case of superelliptic curves with singular points that are rational over the field of definition, and the case of nodal projective plane curves. In each case we present, …
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Phantoms and Exceptional Collections on Rational Surfaces
… concerned with exceptional collections on smooth projective surfaces. Any rational surface over an algebraically closed field admits a full exceptional collection. We extend certain classification results regarding exceptional collections, previously known for del Pezzo surfaces, to the blow-up of …
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Deformations of the Hilbert scheme of points on a del Pezzo surface
… where the del Pezzo surface is the blow up of projective plane at $k$ sufficiently general points; and each of the fibers is of the form that we construct. Our work generalizes results of Nevins-Stafford constructing deformations of the Hilbert scheme of points on the plane, and of Hitchin …
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Towards characterizing morphims between high dimensional hypersurfaces
… In the process, we classify morphisms froin the projective plane to nonsingular cubic threefolds.
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On Projective Planes & Rational Identities
… the presence of an underlying division ring in a projective plane. Supplementing this correspondence is the general theory of intersection theorems, which, restricted to desarguian projective planes P, corresponds precisely to the theory of integral rational identities, restricted to division …
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Techniques in interpolation problems
… as computing the dimension of the space of plane curves of degree d having general multiple points. The general interpolation problem goes back to the origin of algebraic geometry and is still far from being solved. We approach it using algebraic geometry techniques, by systematically …
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Some Results on Vertex-Minimal Triangulations of Manifolds
… only known vertex-minimal triangulation of real projective 4-dimensional space. We show that the 16-vertex complex we describe triangulates RP4 by constructing a 4-dimensional combinatorial sphere which can be easily seen to be a double cover of our complex. In the third chapter, we give two …
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