It was shown by Faltings (1984) Fal84 and Hriljac (1985) Hri85 that the Néron–Tate height of a point on the Jacobian of a curve can be expressed as the self-intersection of a corresponding divisor on ...a regular model of the curve. We make this explicit and use it to give an algorithm for computing Néron–Tate heights on Jacobians of (hyper)elliptic curves. To demonstrate the practicality of our algorithm, we illustrate it by computing Néron–Tate heights on Jacobians of (hyper)elliptic curves of genus 1⩽g⩽9.
We classify real families of minimal degree rational curves that cover an embedded rational surface. A corollary is that if the projective closure of a smooth surface is not biregular isomorphic to ...the projective closure of the unit-sphere, then the set of minimal degree rational curves that cover the surface is either empty or of dimension at most two. Moreover, if these curves are of minimal degree over the real numbers, but not over the complex numbers, then almost all the curves are smooth. Our methods lead to an algorithm that takes as input a real surface parametrization and outputs all real families of rational curves of lowest possible degree that cover the image surface.
In the article questions of stabilization factors of reliability for operation of the ship equipment are considered. The solving research problem aspect and number of similar tasks aimed at ...increasing the reliability of ship’s power plants (SPP), it is necessary to assess the degree of impact of various factors on the operation of the SPP. The work of the engine with loads is presented. Models and expressions for optimizing the computation process are presented. The outcome of a comparative analysis of resource efficiency and energy efficiency are demonstrated in the implementation of the proposed hardware models on FPGA. The calculate is performed on the maritime parameters of realistic situation.
Predmet su rada četiri kameje iz Arheološkog muzeja Istre. Jedna prikazuje portret cara Nerona, dvije prikazuju glave žena s grčkom frizurom, a jedna prikazuje glavu Minerve sa šljemom. Prema izboru ...i oblikovanju motiva, na temelju usporedbe s objavljenim kamejama iz drugih zbirki, moguće je pretpostaviti okvirno vrijeme nastanka kameja i analizirati poruku koju nose. Kameju s Neronovim portretom moguće je povezati s radioničkim središtem u Rimu, dok za ostale nije moguće utvrditi radioničko porijeklo.
Structural and mechanical analyses of rock mass are key components for rock slope stability assessment. The complementary use of photogrammetric techniques and numerical models coupling discrete ...fracture networks with the discrete element method (DEM) provides a methodology that can be applied to assess the mechanical behaviour of realistic three-dimensional (3D) configurations for which fracture persistence cannot be assumed. A real case has been studied to show the complete methodology from the acquisition of the photogrammetric data to the numerical modelling of the potential progressive failure process occurring in the rock mass. Using a 3D mapping system and its associated structural mapping tool Sirovision, the topography and the discontinuity set of an unstable rock block located in a limestone layer of the Mount Néron, located in the French Alps, were imported into a DEM code specially enhanced for the modelling of pre-fractured rock masses. A stability analysis has been carried out, emphasizing the contribution of rock bridge failure through a mixed shear-tensile failure process to the generation of new failure surfaces. This addresses limitations in methodologies using only shear strength reduction method. It is believed that the proposed methodology can strengthen the basis for a more comprehensive stability analysis of complex fractured rock slopes.
Let C/K be a curve of genus 2 over an arbitrary field K. The first part of this two-part paper established a bijection between the set of equivalence classes of the elliptic subcovers of C/K and the ...set of certain primitive representations of an intrinsic quadratic form qC called the refined Humbert invariant. This second part explains how to compute the refined Humbert invariant explicitly from a presentation of the Jacobian variety JC of C.
K3 surfaces and sphere packings SHIODA, Tetsuji
Journal of the Mathematical Society of Japan,
10/2008, Letnik:
60, Številka:
4
Journal Article
Recenzirano
Odprti dostop
We determine the structure of the Mordell-Weil lattice, Néron-Severi lattice and the lattice of transcendental cycles for certain elliptic K3 surfaces. We find that such questions from algebraic ...geometry are closely related to the sphere packing problem, and a key ingredient is the use of the sphere packing bounds in establishing geometric results.
The Néron model over the Igusa curves Liedtke, Christian; Schröer, Stefan
Journal of number theory,
10/2010, Letnik:
130, Številka:
10
Journal Article
Recenzirano
Odprti dostop
We analyze the geometry of rational
p-division points in degenerating families of elliptic curves in characteristic
p. We classify the possible Kodaira symbols and determine for the Igusa moduli ...problem the reduction type of the universal curve. Special attention is paid to characteristic 2 and 3, where wild ramification and stacky phenomena show up.
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