Double cover K3 surfaces of Hirzebruch surfaces

2021 ◽  
Vol 21 (2) ◽  
pp. 221-225
Author(s):  
Taro Hayashi
Keyword(s):  
Rational Surface ◽  
K3 Surfaces ◽  
Double Cover ◽  
Double Covering ◽  
Smooth Surfaces ◽  
Branch Locus ◽  
Hirzebruch Surfaces ◽  
Double Covers

Abstract General K3 surfaces obtained as double covers of the n-th Hirzebruch surfaces with n = 0, 1, 4 are not double covers of other smooth surfaces. We give a criterion for such a K3 surface to be a double covering of another smooth rational surface based on the branch locus of double covers and fibre spaces of Hirzebruch surfaces.

Double Covers and Metastable Immersions of Spheres

1974 ◽  
Vol 26 (1) ◽  
pp. 145-176 ◽  
Author(s):  
Robert Wells
Keyword(s):  
Vector Bundle ◽  
Line Bundle ◽  
Projective Space ◽  
Unit Sphere ◽  
Real Line ◽  
Double Cover ◽  
Sphere Bundle ◽  
Canonical Line Bundle ◽  
Projective Space Bundle ◽  
Double Covers

The real line will be R, Euclidean n-space will be Rn, the unit ball in Rn will be En, the unit sphere in Rn+1 will be Sn, and real projective n-space will be Pn. The canonical line bundle associated with the double cover Sn → Pn will be ηn. If γ is a vector bundle, E(γ) will be its associated cell bundle, S(γ) its associated sphere bundle, P(γ) its associated projective space bundle (P(γ) = S(γ) / (-1)) and T(γ) = E(γ)/S(γ) its Thorn space.

K3 surfaces from configurations of six lines in $\mathbb{P}^{2}$ and mirror symmetry II—$\lambda _{K3}$-functions

2019 ◽  
Author(s):  
Shinobu Hosono ◽  
Bong H Lian ◽  
Shing-Tung Yau
Keyword(s):  
Moduli Space ◽  
Mirror Symmetry ◽  
Theta Functions ◽  
K3 Surfaces ◽  
Double Cover ◽  
Special Boundary ◽  
Higher Dimensional ◽  
Genus 2 ◽  
Local Solutions

Abstract We continue our study on the hypergeometric system $E(3,6)$ that describes period integrals of the double cover family of K3 surfaces. Near certain special boundary points in the moduli space of the K3 surfaces, we construct the local solutions and determine the so-called mirror maps expressing them in terms of genus 2 theta functions. These mirror maps are the K3 analogues of the elliptic $\lambda $-function. We find that there are two nonisomorphic definitions of the lambda functions corresponding to a flip in the moduli space. We also discuss mirror symmetry for the double cover K3 surfaces and their higher dimensional generalizations. A follow-up paper will describe more details of the latter.

scholarly journals On Cartesian Products of Orthogonal Double Covers

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
R. El Shanawany ◽  
M. Higazy ◽  
A. El Mesady
Keyword(s):  
Cartesian Product ◽  
Bipartite Graphs ◽  
Double Cover ◽  
Cartesian Products ◽  
Double Covers ◽  
Complete Bipartite Graphs ◽  
Orthogonal Double Cover

LetHbe a graph onnvertices and𝒢a collection ofnsubgraphs ofH, one for each vertex, where𝒢is an orthogonal double cover (ODC) ofHif every edge ofHoccurs in exactly two members of𝒢and any two members share an edge whenever the corresponding vertices are adjacent inHand share no edges whenever the corresponding vertices are nonadjacent inH. In this paper, we are concerned with the Cartesian product of symmetric starter vectors of orthogonal double covers of the complete bipartite graphs and using this method to construct ODCs by new disjoint unions of complete bipartite graphs.

scholarly journals Signed Cycle Double Covers

10.37236/6760 ◽  
2018 ◽  
Vol 25 (4) ◽  
Author(s):  
Lingsheng Shi ◽  
Zhang Zhang
Keyword(s):  
Double Cover ◽  
Negative Sign ◽  
Signed Graph ◽  
Weak Version ◽  
Cycle Cover ◽  
Double Covers ◽  
Bridgeless Graph

The cycle double cover conjecture states that every bridgeless graph has a collection of cycles which together cover every edge of the graph exactly twice. A signed graph is a graph with each edge assigned by a positive or a negative sign. In this article, we prove a weak version of this conjecture that is the existence of a signed cycle double cover for all bridgeless graphs. We also show the relationships of the signed cycle double cover and other famous conjectures such as the Tutte flow conjectures and the shortest cycle cover conjecture etc.

scholarly journals Minimal permutation representations of the two double covers of Sn

1996 ◽  
Vol 39 (2) ◽  
pp. 285-289
Author(s):  
John Brinkman
Keyword(s):  
Finite Group ◽  
Positive Integer ◽  
Symmetric Group ◽  
Double Cover ◽  
Permutation Representation ◽  
Double Covers ◽  
A Finite Group

Let G be a finite group and denote by µ(G) (see [2]) the least positive integer m such that G has a faithful permutation representation in the symmetric group of degree m. This note considers the value of µ(G) when G is a double cover of the symmetric group.

scholarly journals Strange Duality on Rational Surfaces II: Higher-Rank Cases

2018 ◽  
Vol 2020 (10) ◽  
pp. 3153-3200 ◽  
Author(s):  
Yao Yuan
Keyword(s):  
Exact Sequence ◽  
Moduli Space ◽  
Chern Class ◽  
Rational Surface ◽  
Rational Surfaces ◽  
One Dimensional ◽  
Hirzebruch Surfaces ◽  
Duality Map ◽  
Higher Rank ◽  
Strange Duality

Abstract We study Le Potier’s strange duality conjecture on a rational surface. We focus on the strange duality map $SD_{c_n^r,L}$ that involves the moduli space of rank $r$ sheaves with trivial 1st Chern class and 2nd Chern class $n$, and the moduli space of one-dimensional sheaves with determinant $L$ and Euler characteristic 0. We show there is an exact sequence relating the map $SD_{c_r^r,L}$ to $SD_{c^{r-1}_{r},L}$ and $SD_{c_r^r,L\otimes K_X}$ for all $r\geq 1$ under some conditions on $X$ and $L$ that applies to a large number of cases on $\mathbb{P}^2$ or Hirzebruch surfaces. Also on $\mathbb{P}^2$ we show that for any $r>0$, $SD_{c^r_r,dH}$ is an isomorphism for $d=1,2$, injective for $d=3,$ and moreover $SD_{c_3^3,rH}$ and $SD_{c_3^2,rH}$ are injective. At the end we prove that the map $SD_{c_n^2,L}$ ($n\geq 2$) is an isomorphism for $X=\mathbb{P}^2$ or Fano rational-ruled surfaces and $g_L=3$, and hence so is $SD_{c_3^3,L}$ as a corollary of our main result.

Poincaré Transversality for Double Covers

1978 ◽  
Vol 30 (6) ◽  
pp. 1319-1330 ◽  
Author(s):  
I. Hambleton ◽  
R. J. Milgram
Keyword(s):  
Homotopy Class ◽  
Double Cover ◽  
Poincaré Duality ◽  
Poincare Duality ◽  
Double Covers

Let π: X’ —” X be a double cover of 2n-dimensional Poincaré duality (PD) spaces. The double cover is a fibering so it is classified by a map f: X → RP1+1(l ≫ n). If the homotopy class of f contains a representative which is Poincaré transverse [5] to RPl ⊂ RPl+1, we say that w is Poincarésplit-table.

scholarly journals Double covers of Pn as very ample divisors

1995 ◽  
Vol 137 ◽  
pp. 1-32 ◽  
Author(s):  
Antonio Lanteri ◽  
Marino Palleschi ◽  
Andrew J. Sommese
Keyword(s):  
Hyperelliptic Curve ◽  
Double Cover ◽  
General Question ◽  
The Third ◽  
Double Covers ◽  
Classical Subject ◽  
Hyperplane Sections ◽  
Ample Divisors

The classical subject of surfaces containing a hyperelliptic curve (here a double cover of P1) among their hyperplane sections was settled some years ago by the third author and Van de Ven [SV] (see also [Se], [Io]). This paper is devoted to answering the following general question arising very naturally from that problem.

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