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Showing 1 to 20 of 33 for “"Jacobians"”.
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Computing canonical heights on Jacobians
… the explicit computation of canonical heights on Jacobians of smooth projective curves. Building on an existing algorithm due to Flynn and Smart with modifications by Stoll we generalize efficient methods for the computation of canonical heights on elliptic curves to the case of Jacobian surfaces. …
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Arithmetic properties and decomposability of Jacobians
… of methods used to study the decomposability of Jacobians of curves over the complex numbers. This involves studying the action of a finite group on an abelian variety in general. Next, we use methods for point counting properties of curves over finite fields to study the decomposability of …
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On the Orders of Jacobians of Hyperelliptic Curves
… to efficiently perform group operations in Jacobians of hyperelliptic curves and methods of finding their orders. We conclude by generalizing some heuristics from the case of genus 1 to genus 2 and beyond.
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Elliptic factors in Jacobians of low genus curves
Submitted by Sarah Shreeves (sshreeve@illinois.edu) on 2013-12-02T16:48:35Z No. of bitstreams: 1 paulhus_jennifer_ellipticfactors.pdf: 1394646 bytes, checksum: 2757c22b96c61ee99998a8b121347657 (MD5)
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Graded Lie Algebras, Compactified Jacobians and Arithmetic Statistics
… picture and show that $2$-Selmer elements of the Jacobians of the smooth curves in each family can be parametrised by integral orbits of the corresponding representation. Using geometry-of-numbers techniques, we deduce statistical results on the arithmetic of these curves. We prove these results …
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Compactified Jacobians of integral curves with double points
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1997.
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Orbifold points on Teichmüller curves and Jacobians with complex multiplication
For each integer D >/= 5 with D =/- 0 or 1 mod 4, the Weierstrass curve WD is an algebraic curve and a finite volume hyperbolic orbifold which admits an algebraic and isometric immersion into the moduli space of genus two Riemann surfaces. The Weierstrass curves are the main examples of Teichmüller …
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Explicit division and torsion points on superelliptic Curves and jacobians
In this thesis, I study two problems in the arithmetic of superelliptic curves. By a superelliptic curve, I mean the smooth projective model of the affine plane curve y[superscript n] = f(x) where f(x) is separable, n is coprime to deg(f), and the characteristic of the ground field does not divide …
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Systems of Nonlinear Algebraic Equations Arising in Simulation of Semiconductor Devices
… expensive to use Newton's method. However, the Jacobians of these systems are relatively simple to compute. Hence, it is practical to exploit the properties of these systems and develop a class of Newton-like methods based on splittings of the Jacobians. We state and prove sufficient conditions …
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Linear Forms in Logarithms and Integer Points on Genus-two Curves
… made explicit. We study various properties of Jacobians of genus-two curves, paying particular attention to their embeddings into projective space, and give a method which can be used to find provably all integer points on a genus-two curve. We apply this method to one particular curve by way …
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Método dimensional óptimo de sistemas multicuerpo con restricciones dinámicas: aplicación al diseño de mecanismos planos
… in the designing phase, and well as their Jacobians. The Hessians, which are also required by the sequential quadratic programming algorithm, are calculated from the analytical expressions of the dynamic parameters and Jacobians following the numerical method of finite differences. The …
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Advanced Time Integration Methods with Applications to Simulation, Inverse Problems, and Uncertainty Quantification
… time integration methods that admit approximate Jacobians in the matrix-exponential like operations. EPIRK-W methods extend the W-method theory by [Steihaug and Wofbrandt, Math. Comp. 1979] to preserve their order of accuracy under arbitrary Jacobian approximations. EPIRK-K methods extend the …
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The blowup formula for higher rank Donaldson invariants
… function on a family of genus 2 hyperelliptic Jacobians. Finally, I give a formal argument to explain the appearance of Abelian varieties and theta functions in four dimensional topological field theories.
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Invariants linked to models of curves over discrete valuation rings
… groups and Tamagawa numbers of Neron models of Jacobians using matrix tree theorems from combinatorics. Raynaud gave a description of the component group of the special fiber of the Néron model of a Jacobian, in terms of the multiplicities and intersection numbers of components in the special …
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Diapycnal Mixing and Mass Transfer in Western Boundary Currents
… vorticity fields, shows that this region has low Jacobians associated with high potential vorticity values, as required theoretically for the case of dominant diapycnal mixing. The diapycnal velocity is calculated from the vertical gradient of the Reynolds density flux, this parameterized as …
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Coleman integration for hyperelliptic curves : algorithms and applications
… last two applications concern p-adic heights on Jacobians of hyperelliptic curves. necessary to formulate a p-adic analogue of the Birch and Swinnerton-Dyer conjecture. I conclude by stating the analogue of the Mazur-Tate-Teitelbaum conjecture iii our setting and presenting supporting data.
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Constructing suitable ordinary pairing-friendly curves: A case of elliptic curves and genus two hyperelliptic curves
… new pairing-friendly elliptic curves and Jacobians of genus two hyperelliptic curves which would facilitate an efficient implementation in pairing-based protocols. We aim for curves that have smaller values than ever before reported for di�erent embedding degrees. We also discuss …
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A Streamline Upwind/ Petrov-Galerkin FEM based time-accurate solution of 3D time-domain Maxwell's equations for dispersive materials
… stabilization matrix derived from the flux Jacobians. Along with this new stabilization parameter, scalability is improved by coupling the equations for the perfectly matched layer with those of Maxwell’s equations. Further efficiency gains are achieved by allowing for a variable number of …
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Numerical simulation of two-dimensional Wolfhard-Parker burner
… Adaptive gridding, numerical evaluation of Jacobians and iterations within time step are implemented for computational efficiency. Numerical results have been obtained for different fuels under different conditions. Comparison with measured data by Smyth et al. (1985) for a buoyancy …
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Automatic Linear and Curvilinear Mesh Generation Driven by Validity Fidelity and Topological Guarantees
… valid and with good quality as measured by their Jacobians. The mathematical proof shows that the meshes generated by our algorithm are guaranteed to be homeomorphic to the input images, and all the elements inside the meshes are guaranteed to be with good quality. Experimental results show that …
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