منابع مشابه
Even Sets of Lines on Quartic Surfaces
5 Classification 10 5.1 Two lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 5.2 Four lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 5.3 Six lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 5.4 Eight lines . . . . . . . . . . . . . . . . . . . . . . . . ....
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It is well known that there is an open three-dimensional subvariety Ms of the Grassmannian of lines in P3 which parametrizes smooth irreducible complex surfaces of degree 4 which are Heisenberg invariant, and each quartic contains 32 lines but only 16 skew lines, being determined by its configuration of lines, are called a double 16. We consider here the problem of visualizing in a computer the...
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We searched up to height 107 for rational points on diagonal quartic surfaces. The computations fill several gaps in earlier lists computed by Pinch, Swinnerton-Dyer, and Bright.
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In 1899, Hutchinson [Hut99] presented a way to obtain a threeparameter family of Hessians of cubic surfaces as blowups of Kummer surfaces. We show that this family consists of those Hessians containing an extra class of conic curves. Based on this, we find the invariant of a cubic surface C in pentahedral form that vanishes if its Hessian is in Hutchinson’s family, and we give an explicit map b...
متن کاملExtending symmetric determinantal quartic surfaces
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.
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ژورنال
عنوان ژورنال: Mathematische Annalen
سال: 2016
ISSN: 0025-5831,1432-1807
DOI: 10.1007/s00208-016-1484-0