The 1729 K3 surface
نویسنده
چکیده
1.1 1729 and Ramanujan Srinivasa Ramanujan is said to have possessed an uncanny memory for idiosyncratic properties of numbers. J. E. Littlewood famously remarked that “everynumber is a personal friend of Ramanujan.” This opinion is supported by the famous story of 1729, the so-called “Hardy–Ramanujan” number after the famous anecdote of G. H. Hardy concerning a visit to the hospital to see his collaborator Srinivasa Ramanujan: (page 12 of [6]):
منابع مشابه
Poleni Curves on Surfaces of Constant Curvature
In the euclidean plane, a regular curve can be defined through its intrinsic equation which relates its curvature k to the arc length s. Elastic plane curves were determined this way. If k(s) = 2α cosh(αs) , the curve is known by the name “la courbe des forçats”, introduced in 1729 by Giovanni Poleni in relation with the tractrix [9]. The above equation is yet meaningful on a surface if one int...
متن کاملOn the number of Enriques quotients of a K3 surface
A K3 surface X is a compact complex surface with KX ∼ 0 and H (X,OX) = 0. An Enriques surface is a compact complex surface with H(Y,OY ) = H (Y,OY ) = 0 and 2KY ∼ 0. The universal covering of an Enriques surface is a K3 surface. Conversely every quotient of a K3 surface by a free involution is an Enriques surface. Here a free involution is an automorphism of order 2 without any fixed points. Th...
متن کاملSymmetric symplectic homotopy K3 surfaces
A study on the relation between the smooth structure of a symplectic homotopy K3 surface and its symplectic symmetries is initiated. A measurement of exoticness of a symplectic homotopy K3 surface is introduced, and the influence of an effective action of a K3 group via symplectic symmetries is investigated. It is shown that an effective action by various maximal symplectic K3 groups forces the...
متن کاملThe Effect of Hydrofluoric Acid Surface Treatment on the Cyclic Fatigue Resistance of K3 NiTi Instruments
The aim of this study was to investigate the effect of 50% hydrofluoric acid (HF) surface treatment on the cyclic fatigue resistance (CFR) of K3 NiTi instruments. Twenty as-received and twenty HF-treated K3 NiTi instruments were compared in CFR. The surface texture and fracture surface of two instrument groups were examined with a scanning electron microscope (SEM). Additionally, any change of ...
متن کاملK3 Surfaces with Nine Cusps
By a K3-surface with nine cusps I mean a surface with nine isolated double points A 2 , but otherwise smooth, such that its minimal desingularisation is a K3-surface. It is shown, that such a surface admits a cyclic triple cover branched precisely over the cusps. This parallels the theorem of Nikulin, that a K3-surface with 16 nodes is a Kummer quotient of a complex torus.
متن کامل