The gonality of curves on a Hirzebruch surface

1996 ◽  
Vol 67 (4) ◽  
pp. 349-352 ◽  
Author(s):  
G. Martens
Keyword(s):  
Hirzebruch Surface

scholarly journals Non Kählerian surfaces with a cycle of rational curves

2021 ◽  
Vol 8 (1) ◽  
pp. 208-222
Author(s):  
Georges Dloussky
Keyword(s):  
Deformation Theory ◽  
Complex Surface ◽  
Rational Curves ◽  
Intersection Form ◽  
Connected Component ◽  
Hirzebruch Surface ◽  
Compact Complex Surface ◽  
A Chain

Abstract Let S be a compact complex surface in class VII0 + containing a cycle of rational curves C = ∑Dj . Let D = C + A be the maximal connected divisor containing C. If there is another connected component of curves C ′ then C ′ is a cycle of rational curves, A = 0 and S is a Inoue-Hirzebruch surface. If there is only one connected component D then each connected component Ai of A is a chain of rational curves which intersects a curve Dj of the cycle and for each curve Dj of the cycle there at most one chain which meets Dj . In other words, we do not prove the existence of curves other those of the cycle C, but if some other curves exist the maximal divisor looks like the maximal divisor of a Kato surface with perhaps missing curves. The proof of this topological result is an application of Donaldson theorem on trivialization of the intersection form and of deformation theory. We apply this result to show that a twisted logarithmic 1-form has a trivial vanishing divisor.

scholarly journals Hilbert schemes of some threefold scrolls over 𝔽e

2016 ◽  
Vol 16 (4) ◽  
Author(s):  
Maria Lucia Fania ◽  
Flaminio Flamini
Keyword(s):  
Hilbert Schemes ◽  
Hirzebruch Surface

AbstractHilbert schemes of suitable smooth, projective threefold scrolls over the Hirzebruch surface 𝔽

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].

scholarly journals On fundamental groups related to the Hirzebruch surface F 1

2008 ◽  
Vol 51 (4) ◽  
pp. 728-745 ◽  
Author(s):  
Michael Friedman ◽  
Mina Teicher
Keyword(s):  
Fundamental Groups ◽  
Hirzebruch Surface

scholarly journals Nef Cones of Nested Hilbert Schemes of Points on Surfaces

2018 ◽  
Vol 2020 (11) ◽  
pp. 3260-3294
Author(s):  
Tim Ryan ◽  
Ruijie Yang
Keyword(s):  
Projective Plane ◽  
Birational Geometry ◽  
K3 Surface ◽  
Hilbert Schemes ◽  
Hirzebruch Surface ◽  
Hirzebruch Surfaces ◽  
Nef Cone

Abstract Let X be the projective plane, a Hirzebruch surface, or a general K3 surface. In this paper, we study the birational geometry of various nested Hilbert schemes of points parameterizing pairs of zero-dimensional subschemes on X. We calculate the nef cone for two types of nested Hilbert schemes. As an application, we recover a theorem of Butler on syzygies on Hirzebruch surfaces.

scholarly journals BOUNDING THE VOLUMES OF SINGULAR WEAK LOG DEL PEZZO SURFACES

2013 ◽  
Vol 24 (13) ◽  
pp. 1350110 ◽  
Author(s):  
CHEN JIANG
Keyword(s):  
Upper Bound ◽  
General Position ◽  
Del Pezzo Surfaces ◽  
Minimal Resolution ◽  
Picard Number ◽  
Hirzebruch Surface ◽  
Del Pezzo Surface ◽  
Blowing Up ◽  
Del Pezzo ◽  
Log Del Pezzo Surfaces

We give an optimal upper bound for the anti-canonical volume of an ϵ-lc weak log del Pezzo surface. Moreover, we consider the relation between the bound of the volume and the Picard number of the minimal resolution of the surface. Furthermore, we consider blowing up several points on a Hirzebruch surface in general position and give some examples of smooth weak log del Pezzo surfaces.

scholarly journals Hilbert scheme of some threefold scrolls over the Hirzebruch surface ${\mathbb F}_1$

2013 ◽  
Vol 65 (4) ◽  
pp. 1243-1272 ◽  
Author(s):  
Gian Mario BESANA ◽  
Maria Lucia FANIA ◽  
Flaminio FLAMINI
Keyword(s):  
Hilbert Scheme ◽  
Hirzebruch Surface
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