Extending symmetric determinantal quartic surfaces
نویسنده
چکیده
We give an explicit construction for the extension of a symmetric determinantal quartic K3 surface to a Fano 6-fold. Remarkably, the moduli of the 6-fold extension are in one-to-one correspondence with the moduli of the quartic surface. As a consequence, we determine a 16-parameter family of surfaces of general type with pg = 1 and K = 2 as weighted complete intersections inside Fano 6-folds.
منابع مشابه
Two-parametric PT-symmetric quartic family
We describe a parametrization of the real spectral locus of the twoparametric family of PT-symmetric quartic oscillators. For this family, we find a parameter region where all eigenvalues are real, extending the results of Dorey, Dunning, Tateo and Shin. MSC: 81Q05, 34M60, 34A05
متن کاملOn polarised class groups of orders in quartic CM-fields
We give an explicit characterisation of pairs of orders in a quartic CM-field that admit the same polarised ideal class group structure. This generalises a simpler result for imaginary quadratic fields. We give applications to computing endomorphism rings of abelian surfaces over finite fields, and extending a completeness result of Murabayashi and Umegaki [13] to a list of abelian surfaces ove...
متن کاملThe Automorphism Groups of Enriques Surfaces Covered by Symmetric Quartic Surfaces
Let S be the (minimal) Enriques surface obtained from the symmetric quartic surface ( P i<j xixj) 2 = kx1x2x3x4 in P with k 6= 0, 4, 36, by taking quotient of the Cremona action (xi) 7→ (1/xi). The automorphism group of S is a semi-direct product of a free product F of four involutions and the symmetric group S4. Up to action of F , there are exactly 29 elliptic pencils on S. The automorphism g...
متن کاملSmooth Kummer Surfaces in Projective Three-space
In this note we prove the existence of smooth Kummer surfaces in projective three-space containing sixteen mutually disjoint smooth rational curves of any given degree. Introduction Let X be a smooth quartic surface in projective three-space P. As a consequence of Nikulin’s theorem [6] X is a Kummer surface if and only if it contains sixteen mutually disjoint smooth rational curves. The classic...
متن کاملTENSION QUARTIC TRIGONOMETRIC BÉZIER CURVES PRESERVING INTERPOLATION CURVES SHAPE
In this paper simple quartic trigonometric polynomial blending functions, with a tensionparameter, are presented. These type of functions are useful for constructing trigonometricB´ezier curves and surfaces, they can be applied to construct continuous shape preservinginterpolation spline curves with shape parameters. To better visualize objects and graphics atension parameter is included. In th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009