Kummer surfaces: 200 years of study

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August undefined, 2024

WebKummer surfaces: Let Abe a two-dimensional complex torus, and : A!Abe the involution a! a. This has 16 xed points. A= has only ordinary double point singularities and there are 16 of them. The surface S!A= given by the minimal resolution of A= , obtained by blowing up these 16 points, are K3 surfaces and they are called Kummer surfaces.

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WebK3 surfaces. Kummer surfaces play a central role in the study of K3 surfaces, indeed certain results on K3 surfaces are easier to prove for Kummer surfaces (thanks to their relation with the Abelian surfaces), but can be extended to more general families of K3 surfaces: the most classical example of this is the Torelli theorem, which holds for ... WebOct 16, 2024 · Kummer 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 … termites testing

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WebKummer 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 … WebMar 1, 2024 · An important class of $ K3 $-surfaces is provided by the Kummer surfaces. A Kummer surface is a non-singular model for the quotient of a two-dimensional Abelian variety $ A $ with respect to the automorphism subgroup generated by the sign-change mapping. In particular, the surface given by the equation $ x _ {0} ^ {4} + x _ {1} ^ {4} + x _ … WebMar 24, 2024 · The Kummer surfaces are a family of quartic surfaces given by the algebraic equation (x^2+y^2+z^2-mu^2w^2)^2-lambdapqrs=0, (1) where lambda=(3mu^2-1)/(3 … trick bumble location pc

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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 … WebA 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 … trick buildWebdegree 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 trick bulbapedia

"WebApr 18, 2024 · April 18, 2024 Explicit Nikulin configurations on Kummer surfaces Xavier Roulleau, Alessandra Sarti Page range: 329-340 More Cite this July 3, 2024 Irregular surfaces on hypersurfaces of degree 4 with non-degenerate isolated singularities Daniel Naie Page range: 341-354 More Cite this April 18, 2024 " - Kummer surfaces: 200 years of study

Kummer surfaces: 200 years of study

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WebA special configuration of 12 conics and generalized Kummer surfaces manuscripta mathematica . 10.1007/s00229-021-01334-2 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. …

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WebJul 29, 2024 · The question was studied by several authors, and it was shown that the number of non-isomorphic Kummer structures is finite, but no explicit geometric construction of such structures was given. In a previous paper, we constructed explicitly non isomorphic Kummer structures on some Kummer surfaces. http://www-math.sp2mi.univ-poitiers.fr/~sarti/GarbagnatiSarti_RMJ.pdf

WebDe 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. WebThis 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 University on October 10, 2024 delivered exactly …

WebOct 16, 2024 · Kummer surfaces: 200 years of study October 2024 Authors: Igor Dolgachev University of Michigan Abstract This is a brief history of discovery and later study of … WebKummer surface is algebraic. Kummer surfaces are among classical examples of K3-surfaces (which are simply-connected smooth surfaces with a nowhere-vanishing holomorphic 2-form), and play a crucial role in the theory of K3-surfaces. In a sense, all Kummer surfaces (resp. algebraic Kummer surfaces) form a 4 (resp. 3)-dimensional …

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 …

WebErnst Eduard Kummer, (born January 29, 1810, Sorau, Brandenburg, Prussia [Germany]—died May 14, 1893, Berlin), German mathematician whose introduction of ideal numbers, which … termites that flyWebKummer 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 … termites that look like antsWebSep 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... termite stickersWebMar 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] termites tibiaWebKummer 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 ... trick butterfliesWebThe 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 … termite sticksWebAlgebraic Surfaces; Of a Cubic Space Curve and a Quadric Surface* New Trends in Arithmetic and Geometry of Algebraic Surfaces; The Classification of Surfaces and Other Varieties; Kummer Surfaces: 200 Years of Study; Arxiv:0907.0454V3 [Math.GT] 14 Apr 2016 Ler Fgeneral of Algebra 4-Manifolds; CLASSIFICATION of COMPLEX ALGEBRAIC … trick but treat 意味