Kummer surfaces: 200 years of study
WebThe Kummer involution has 16 fixed points: the 16 2-torsion point of the Jacobian, and they are the 16 singular points of the quartic surface. Resolving the 16 double points of the quotient of a (possibly …
Kummer surfaces: 200 years of study
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Webdegree 2 K3 surface and our Theorem 1.1 follows from [HKT13]. However there are a few di culties when one tries to implement [HKT13] for Kummer surfaces. The rst is that it is known that if we let X be the Kummer surface associated to an abelian surface A, then its Kuga{Satake variety is isogeneous to a power of A. However, to WebMar 13, 2024 · Abstract: We show how to use the arithmetic of the Kummer surface associated to the Jacobian of a hyperelliptic curve to study the primality of integers of the form $4 m^2\cdot 5^n-1$. Subjects: Algebraic Geometry (math.AG); Number Theory (math.NT) Cite as: arXiv:2003.06490 [math.AG]
Webbetween fast Kummer surfaces that, in part, inspired the present work. – Being able to study Kummer surface arithmetic as a viable alternative in the supersingular isogeny landscape is made easier by virtue of the fact that state-of-the-art SIDH implementations already work entirely in the Kummer WebResolving the 16 double points of the quotient of a (possibly nonalgebraic) torus by the Kummer involution gives a K3 surfacewith 16 disjoint rational curves; these K3 surfaces are also sometimes called Kummer surfaces. …
WebNov 1, 2024 · Kummer surfaces and quadric line complexes in characteristic two Preprint Full-text available Jan 2024 Toshiyuki Katsura Shigeyuki Kondo View Show abstract ... It … WebKummer's geometric period was one when he devoted himself to the study of the ray systems that Hamilton had examined, but Kummer treated these problems algebraically. He also discovered the fourth order surface, now named after him, based on the singular surface of the quadratic line complex.
WebKummer Surfaces: 200 Years of Study; Arxiv:0907.0454V3 [Math.GT] 14 Apr 2016 Ler Fgeneral of Algebra 4-Manifolds; CLASSIFICATION of COMPLEX ALGEBRAIC SURFACES …
WebSep 29, 2009 · This paper classifies Enriques surfaces whose K3-cover is a fixed Picard-general Jacobian Kummer surface. There are exactly 31 such surfaces. We describe the free involutions which give... successful companies that pivotedWebDe nition 2.2. A K3 surface is a compact connected complex manifold X of dimension two such that its canonical bundle is trivial and H1(X;O X) = 0. Corrolary 2.3. Kummer surface is a K3 surface. Theorem 2.4. Any two complex K3 surfaces are di eomorphic. Proposition 2.5. All nonsingular curves on a K3 surface have even inter-section numbers. Proof. successful completion of trainingWebIn this paper we study generalized Kummer varieties, showing that an automorphism leaving invariant the exceptional divisor is a natural automorphism, i.e. is induced by an automorphism of the underlying abelian surface. A proof of the corresponding result for the Hilbert schemes of points on K3 surfaces is given in [5]. successful community health worker programsWebKummer Surfaces: 200 Years of Study. Igor Dolgachev. The fascinating story about the Kummer surface starts from material where double refraction occurs: a ray of light the discovery by Augustin-Jean Fresnel in 1822 of the equa- splits into two, traveling at the same speed along different tion describing the propagation of light in an optically ... painting irises acrylicWebKummer surfaces: 200 years of study This is a brief history of discovery and later study of Kummer surfaces. The article is based on the author's Oliver Club talk at Cornell … painting in winter interiorWebA Kummer surface is the minimal desingularization of the surface Tji, where T is a complex torus of dimension 2 and i the involution auto-morphism on T. T is an abelian surface if … successful connection to redis-server翻译WebX. Then we study the corresponding Enriques surfaces S/γ. We also describe in detail the remarkable properties of the most symmetric Kummer quartic, which we call the Cefalu´ quartic. We also investigate the Kummer quartic surfaces whose associated Abelian surface is isogenous to a product of elliptic curves through successful completion with merit