On Galois covers of Hirzebruch surfaces

1996 ◽  
Vol 305 (1) ◽  
pp. 493-539 ◽  
Author(s):  
B. Moishezon ◽  
A. Robb ◽  
M. Teicher
Keyword(s):  
Hirzebruch Surfaces ◽  
Galois Covers

THE FUNDAMENTAL GROUP OF THE GALOIS COVER OF HIRZEBRUCH SURFACE F1(2, 2)

2007 ◽  
Vol 17 (03) ◽  
pp. 507-525 ◽  
Author(s):  
MEIRAV AMRAM ◽  
MINA TEICHER ◽  
UZI VISHNE
Keyword(s):  
Fundamental Group ◽  
Hirzebruch Surface ◽  
Generic Projection ◽  
Galois Cover ◽  
Hirzebruch Surfaces ◽  
Galois Covers ◽  
Branch Curve

This paper is the second in a series of papers concerning Hirzebruch surfaces. In the first paper in this series, the fundamental group of Galois covers of Hirzebruch surfaces Fk(a, b), where a, b are relatively prime, was shown to be trivial. For the general case, the conjecture stated that the fundamental group is [Formula: see text] where c = gcd (a, b) and n = 2ab + kb2. In this paper, we degenerate the Hirzebruch surface F1(2, 2), compute the braid monodromy factorization of the branch curve in ℂ2, and verify that, in this case, the conjecture holds: the fundamental group of the Galois cover of F1(2, 2) with respect to a generic projection is isomorphic to [Formula: see text].

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.

scholarly journals Topological Formulae for the Zeroth Cohomology of Line Bundles on del Pezzo and Hirzebruch Surfaces

2021 ◽  
Vol 8 (1) ◽  
pp. 223-229
Author(s):  
Callum R. Brodie ◽  
Andrei Constantin ◽  
Rehan Deen ◽  
Andre Lukas
Keyword(s):  
Topological Index ◽  
Line Bundles ◽  
Hirzebruch Surfaces ◽  
Del Pezzo

Abstract We show that the zeroth cohomology of effective line bundles on del Pezzo and Hirzebruch surfaces can always be computed in terms of a topological index.

scholarly journals Decomposing Jacobians Via Galois covers

2021 ◽  
pp. 1-23
Author(s):  
Davide Lombardo ◽  
Elisa Lorenzo García ◽  
Christophe Ritzenthaler ◽  
Jeroen Sijsling
Keyword(s):  
Galois Covers

Specializations of Galois covers of the line

2011 ◽  
Author(s):  
Pierre Dèbes ◽  
Nour Ghazi
Keyword(s):  
Galois Covers

scholarly journals Analytic torsion of Hirzebruch surfaces

2006 ◽  
Vol 335 (1) ◽  
pp. 221-247 ◽  
Author(s):  
Christophe Mourougane
Keyword(s):  
Analytic Torsion ◽  
Hirzebruch Surfaces

�tale Galois covers of affine smooth curves

1995 ◽  
Vol 120 (1) ◽  
pp. 555-578 ◽  
Author(s):  
Florian Pop
Keyword(s):  
Smooth Curves ◽  
Galois Covers
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