Example of a transcendental 3-torsion Brauer-Manin obstruction on a diagonal quartic surface

2013 ◽  
pp. 447-459 ◽  
Author(s):  
T. Preu
Keyword(s):  
Quartic Surface

scholarly journals Two algebraic deformations of a K3 surface

1981 ◽  
Vol 82 ◽  
pp. 1-26
Author(s):  
Daniel Comenetz
Keyword(s):  
Hyperelliptic Curve ◽  
Double Cover ◽  
Rational Curves ◽  
K3 Surface ◽  
Quartic Surface ◽  
Quadric Cone ◽  
Birational Model ◽  
Affine Line ◽  
Characteristic 2 ◽  
General Member

Let X be a nonsingular algebraic K3 surface carrying a nonsingular hyperelliptic curve of genus 3 and no rational curves. Our purpose is to study two algebraic deformations of X, viz. one specialization and one generalization. We assume the characteristic ≠ 2. The generalization of X is a nonsingular quartic surface Q in P3 : we wish to show in § 1 that there is an irreducible algebraic family of surfaces over the affine line, in which X is a member and in which Q is a general member. The specialization of X is a surface Y having a birational model which is a ramified double cover of a quadric cone in P3.

The minimal resolution conjecture on a general quartic surface in P3

2019 ◽  
Vol 223 (4) ◽  
pp. 1456-1471
Author(s):  
M. Boij ◽  
J. Migliore ◽  
R.M. Miró-Roig ◽  
U. Nagel
Keyword(s):  
Minimal Resolution ◽  
Quartic Surface

scholarly journals VECTOR BUNDLES, DUALITIES AND CLASSICAL GEOMETRY ON A CURVE OF GENUS TWO

2007 ◽  
Vol 18 (05) ◽  
pp. 535-558 ◽  
Author(s):  
QUANG MINH NGUYEN
Keyword(s):  
Vector Bundles ◽  
Double Cover ◽  
Line Bundles ◽  
Theta Divisor ◽  
Quartic Surface ◽  
Stable Vector Bundles ◽  
Symmetric Configuration ◽  
Classical Geometry ◽  
Genus Two ◽  
Linear Sections

Let C be a curve of genus two. We denote by [Formula: see text] the moduli space of semi-stable vector bundles of rank 3 and trivial determinant over C, and by Jd the variety of line bundles of degree d on C. In particular, J1 has a canonical theta divisor Θ. The space [Formula: see text] is a double cover of ℙ8 = |3Θ| branched along a sextic hypersurface, the Coble sextic. In the dual [Formula: see text], where J1 is embedded, there is a unique cubic hypersurface singular along J1, the Coble cubic. We prove that these two hypersurfaces are dual, inducing a non-abelian Torelli result. Moreover, by looking at some special linear sections of these hypersurfaces, we can observe and reinterpret some classical results of algebraic geometry in a context of vector bundles: the duality of the Segre–Igusa quartic with the Segre cubic, the symmetric configuration of 15 lines and 15 points, the Weddle quartic surface and the Kummer surface.

A Cyclic Involution of Period Eleven

1951 ◽  
Vol 3 ◽  
pp. 155-158
Author(s):  
W. R. Hutcherson
Keyword(s):  
Quartic Surface ◽  
Cubic Surfaces

In two earlier papers * the writer discussed involutions of periods five and seven on certain cubic surfaces in S3. In this paper, a quartic surface containing a cyclic involution of period eleven is considered. The surface

scholarly journals A type of periodicity of certain quartic surfaces

1942 ◽  
Vol 7 (1) ◽  
pp. 73-80 ◽  
Author(s):  
W. L. Edge
Keyword(s):  
Present Note ◽  
Quartic Surface ◽  
Periodic Property ◽  
A Chain ◽  
Quartic Surfaces ◽  
Do So

The following pages have been written in consequence of reading some paragraphs by Reye, in which he obtains, from a quartic surface, a chain of contravariant quartic envelopes and of covariant quartic loci. This chain is, in general, unending; but Reye at once foresaw the possibility of the quartic surface being such that the chain would be periodic. The only example which he gave of periodicity being realised was that in which the quartic surface was a repeated quadric. It is reasonable to suppose that, had he been able to do so, he would have chosen some surface which had the periodic property without being degenerate; in the present note two such surfaces are signalised.

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