scholarly journals COMPUTINGL-FUNCTIONS AND SEMISTABLE REDUCTION OF SUPERELLIPTIC CURVES

2016 ◽  
Vol 59 (1) ◽  
pp. 77-108 ◽  
Author(s):  
IRENE I. BOUW ◽  
STEFAN WEWERS
Keyword(s):  
Explicit Description ◽  
Semistable Reduction ◽  
Residue Characteristic ◽  
Superelliptic Curves ◽  
Stable Reduction

AbstractWe give an explicit description of the stable reduction of superelliptic curves of the formyn=f(x) at primes$\mathfrak{p}$whose residue characteristic is prime to the exponentn. We then use this description to compute the localL-factor and the exponent of conductor at$\mathfrak{p}$of the curve.

scholarly journals Invariants for trees of non-archimedean polynomials and skeleta of superelliptic curves

2022 ◽  
Author(s):  
Paul Alexander Helminck
Keyword(s):  
Elliptic Curve ◽  
Moduli Spaces ◽  
Newton Polygon ◽  
Semistable Reduction ◽  
Plücker Coordinates ◽  
Different Types ◽  
Residue Characteristic ◽  
Superelliptic Curves

AbstractIn this paper we generalize the j-invariant criterion for the semistable reduction type of an elliptic curve to superelliptic curves X given by $$y^{n}=f(x)$$ y n = f ( x ) . We first define a set of tropical invariants for f(x) using symmetrized Plücker coordinates and we show that these invariants determine the tree associated to f(x). This tree then completely determines the reduction type of X for n that are not divisible by the residue characteristic. The conditions on the tropical invariants that distinguish between the different types are given by half-spaces as in the elliptic curve case. These half-spaces arise naturally as the moduli spaces of certain Newton polygon configurations. We give a procedure to write down their equations and we illustrate this by giving the half-spaces for polynomials of degree $$d\le {5}$$ d ≤ 5 .

The Movement of Ezekiel’s “Living Beings” in 4Q405 Shirot ‘Olat Hashabbat. Part II: The Twelfth Song

2018 ◽  
Vol 27 (1) ◽  
Author(s):  
Annette Evans
Keyword(s):  
Explicit Description ◽  
Plural Form ◽  
The Law ◽  
Mount Sinai

In this article descriptions of angelic movement in the Twelfth Song are compared to descriptions of such activity arising from the throne of God in Ezekiel’s vision in Ezekiel 1 and 10, and to that in the Seventh Song as contained in scroll 4Q403. The penultimate Twelfth Song of the Songs of the Sabbath Sacrifice culminates in a more explicit description of angelic messenger activity and in other nuances. The Twelfth Song was intended to be read on the Sabbath immediately following Shavu’ot, when the traditional synagogue reading is Ezekiel 1 and Exodus 19–20. The possible significance for the author of Songs of the Sabbath Sacrifice of the connection between the giving of the Law at Mount Sinai and Ezekiel’s vision where merkebah thrones and seats appear in the plural form is considered in the conclusion

Strategic Scripts and Nuclear Disarmament

2018 ◽  
Author(s):  
Matthew Harries ◽  
Benedict Wilkinson
Keyword(s):  
Nuclear Weapons ◽  
Analytical Tool ◽  
The Other ◽  
Nuclear Disarmament ◽  
Stable Reduction ◽  
The Way

This chapter spans Freedman’s earliest focus on nuclear weapons and his development of strategic scripts as an analytical tool over three decades later. It discusses the way in which opposing logics of disarmament and armament co-existed in relation to nuclear weapons. It deploys the notion of strategic scripts to explain the contradictions inherent in approaches to nuclear disarmament, developing the concept of strategic scripts as it does so. The notion of scripts can be used to explore and even to promote nuclear disarmament. Two scripts, one of ‘stable reduction’, the other of ‘disarmament’, each serve to frame thinking. These scripts and the interactions they generate facilitate understanding of the way in which opposite instinctive reactions and, stemming from these, scripts about nuclear weapons co-exist, but are fragile as either an analytical or a strategic tool.

scholarly journals Polynomial identities related to special Schubert varieties

2021 ◽  
Author(s):  
Francesca Cioffi ◽  
Davide Franco ◽  
Carmine Sessa
Keyword(s):  
Arbitrary Number ◽  
Schubert Variety ◽  
Decomposition Theorem ◽  
Point Of View ◽  
Explicit Description ◽  
Intersection Cohomology ◽  
Schubert Varieties ◽  
Polynomial Identities ◽  
Poincaré Polynomial

AbstractLet $$\mathcal S$$ S be a single condition Schubert variety with an arbitrary number of strata. Recently, an explicit description of the summands involved in the decomposition theorem applied to such a variety has been obtained in a paper of the second author. Starting from this result, we provide an explicit description of the Poincaré polynomial of the intersection cohomology of $$\mathcal S$$ S by means of the Poincaré polynomials of its strata, obtaining interesting polynomial identities relating Poincaré polynomials of several Grassmannians, both by a local and by a global point of view. We also present a symbolic study of a particular case of these identities.

The Finite-dimensional Modular Lie Superalgebra Γ

2010 ◽  
Vol 17 (03) ◽  
pp. 525-540 ◽  
Author(s):  
Xiaoning Xu ◽  
Yongzheng Zhang ◽  
Liangyun Chen
Keyword(s):  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Explicit Description ◽  
Cartan Type ◽  
Modular Lie Superalgebra ◽  
New Family ◽  
Finite Dimensional ◽  
Derivation Superalgebra ◽  
Modular Lie Superalgebras

A new family of finite-dimensional modular Lie superalgebras Γ is defined. The simplicity and generators of Γ are studied and an explicit description of the derivation superalgebra of Γ is given. Moreover, it is proved that Γ is not isomorphic to any known Lie superalgebra of Cartan type.

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