Regular Algebraic Surfaces, Ramification Structures and Projective Planes

2015 ◽  
pp. 15-33 ◽  
Author(s):  
N. Barker ◽  
N. Boston ◽  
N. Peyerimhoff ◽  
A. Vdovina
Keyword(s):  
Projective Planes ◽  
Algebraic Surfaces

scholarly journals Q_l-cohomology projective planes and singular Enriques surfaces in characteristic two

2019 ◽  
Vol Volume 3 ◽  
Author(s):  
Matthias Schütt
Keyword(s):  
Projective Planes ◽  
Rational Curves ◽  
Existence Results ◽  
Algebraic Surfaces ◽  
Prime Field ◽  
One Dimensional ◽  
Enriques Surfaces ◽  
Characteristic Two ◽  
The Given ◽  
Root Types

We classify singular Enriques surfaces in characteristic two supporting a rank nine configuration of smooth rational curves. They come in one-dimensional families defined over the prime field, paralleling the situation in other characteristics, but featuring novel aspects. Contracting the given rational curves, one can derive algebraic surfaces with isolated ADE-singularities and trivial canonical bundle whose Q_l-cohomology equals that of a projective plane. Similar existence results are developed for classical Enriques surfaces. We also work out an application to integral models of Enriques surfaces (and K3 surfaces). Comment: 24 pages; v3: journal version, correcting 20 root types to 19 and ruling out the remaining type 4A_2+A_1 (in new section 11)

Complex Algebraic Surfaces

1996 ◽  
Author(s):  
Arnaud Beauville
Keyword(s):  
Algebraic Surfaces

Spiky projective planes

1991 ◽  
Vol 257 (1-2) ◽  
pp. 51-55
Author(s):  
D. Johnston
Keyword(s):  
Projective Planes

scholarly journals On submaximal curves in fake projective planes

2021 ◽  
Vol 225 (10) ◽  
pp. 106709
Author(s):  
Piotr Pokora ◽  
Halszka Tutaj-Gasińska
Keyword(s):  
Projective Planes

4-Dimensional projective planes of Lenz type III

1972 ◽  
Vol 1 (1) ◽  
Author(s):  
Helmut Salzmann
Keyword(s):  
Projective Planes ◽  
Type Iii

scholarly journals Maximal arcs in projective planes of order 16 and related designs

2019 ◽  
Vol 19 (3) ◽  
pp. 345-351 ◽  
Author(s):  
Mustafa Gezek ◽  
Vladimir D. Tonchev ◽  
Tim Wagner
Keyword(s):  
Projective Plane ◽  
Projective Planes ◽  
Maximal Arcs ◽  
Even Order

Abstract The resolutions and maximal sets of compatible resolutions of all 2-(120,8,1) designs arising from maximal (120,8)-arcs, and the 2-(52,4,1) designs arising from previously known maximal (52,4)-arcs, as well as some newly discovered maximal (52,4)-arcs in the known projective planes of order 16, are computed. It is shown that each 2-(120,8,1) design associated with a maximal (120,8)-arc is embeddable in a unique way in a projective plane of order 16. This result suggests a possible strengthening of the Bose–Shrikhande theorem about the embeddability of the complement of a hyperoval in a projective plane of even order. The computations of the maximal sets of compatible resolutions of the 2-(52,4,1) designs associated with maximal (52,4)-arcs show that five of the known projective planes of order 16 contain maximal arcs whose associated designs are embeddable in two nonisomorphic planes of order 16.

scholarly journals Configurations in projective planes and quadrilateral-star Ramsey numbers

2008 ◽  
Vol 308 (17) ◽  
pp. 3986-3991 ◽  
Author(s):  
E.L. Monte Carmelo
Keyword(s):  
Projective Planes ◽  
Ramsey Numbers

Comments on ‘Global dynamics of the generalized Lorenz systems having invariant algebraic surfaces’

2014 ◽  
Vol 266 ◽  
pp. 80-82 ◽  
Author(s):  
Antonio Algaba ◽  
Fernando Fernández-Sánchez ◽  
Manuel Merino ◽  
Alejandro J. Rodríguez-Luis
Keyword(s):  
Algebraic Surfaces ◽  
Global Dynamics ◽  
Invariant Algebraic Surfaces
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