Global ETD Search
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Showing 1 to 13 of 13 for “"Intersection theory"”.
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Enumerative problems in intersection theory
… develop and describe some of the basic tools of intersection theory in algebraic geometry. Some classical enumerative problems are then solved using these methods. In particular, we discuss the Fano variety of a cubic in surface in P3 , determinantal varieties, and the number of conics tangent to …
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Tropical Intersection Theory on Moduli Stack of Curve Coverings
… twisted tropical curves). We define the tropical intersection theory on $\mathfrac{M}_\eta^\text{trop}$ and show that the tropical intersection theory agrees with the intersection theory on the moduli stack $\bar{\mathfrac{M}}_\eta$ of \'{e}tale covers (i.e., coverings of twisted algebraic …
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The Neron-Tate height and intersection theory on arithmetic surfaces
Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1983.
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Complete Tropical Bezout's Theorem and Intersection Theory in the Tropical Projective Plane
… We provide several different definitions of intersection multiplicity and show that they all agree. Finally, we will use a tropical resultant to determine the intersection multiplicity of points of intersection at infinite distance. Using these new definitions of intersection multiplicity we …
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Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions
… of open Gromov-Witten type invariants based on intersection theory on the moduli space of pseudoholomorphic curves of arbitrary genus with boundary in a Lagrangian submanifold. We assume the Lagrangian submanifold arises as the fixed points of an anti-symplectic involution and has dimension 2 or …
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The Configuration Space of Two Particles Moving on a Graph
… the Betti numbers of this space. We develop an intersection theory for cycles in graphs inspired by the classical intersection theory for cycles in manifolds and we use this to develop an algorithm to calculate the second Betti number of F (Γ,2) for any graph Γ. We also use this intersection …
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Equivariant Chow groups and multiplicities
… for schemes with a torus action and develop the intersection theory related to it. The equivariant intersection theories that have been considered in the past have been the Chow groups and the K-theory of the quotient scheme, as well as the equivariant K-groups of the original scheme. The …
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Higher Siegel-Weil formulae over function fields
… shtukas, and initiated the study of their intersection theory. They proved a higher Siegel-Weil formula in the case of non-degenerate Fourier coefficients, relating the degrees of these cycles to higher derivatives of Siegel-Eisenstein series. In this thesis, we generalize their result in …
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On Different Parametrizations of Feynman Integrals
… touch upon techniques which are related to graph theory and complex analysis. Then we use Intersection Theory to compute the recurrence relations among classes of integrals. We confirm the consistency of these two new approaches using traditional Integration-By-Parts calculations.</p>
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Arithmetic transfers, modularity of arithmetic theta series and geometry of local-global Shimura varieties at parahoric levels
… of explicit test functions to arithmetic intersection numbers of special cycles. The formulation involves a way to resolve the singularity of relevant moduli spaces via natural stratifications and modify derived cycles. They appear naturally in the context of W. Zhang’s relative trace …
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Plane Algebroid Curves in Arbitrary Characteristic
… related to the normalization of the curve. The theory was then adapted to arbitrary algebraically closed field using the so-called Hamburger Noether expansions that take track of the entire desingularization process of the curve. In this work, we will use, instead, the notion of contact order …
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Computing canonical heights on Jacobians
… surfaces. The main tools are the explicit theory of the Kummer surface associated to a Jacobian surface, which we develop in full generality, building on earlier work due to Flynn, and a careful study of the local Néron models of the Jacobian. As a first step for a further generalization to …
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Beyond Stacking: An Exploration of the Impact of Background on Leadership Recruitment and Positional Segregation in Division-I Womens Basketball
… and race/ethnicity (for athletes). Using intersection theory as a framework for understanding the ways in which race, class, and gender function together in the lived experiences of individuals, this study explored the influence that an individual's biographical characteristics have on the …