On the completeness of flat surfaces in
Thomas E. Cecil (1975)
Colloquium Mathematicae
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Thomas E. Cecil (1975)
Colloquium Mathematicae
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Arnaud Beauville (2014)
Journal de l’École polytechnique — Mathématiques
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For a smooth complex projective variety, the rank of the Néron-Severi group is bounded by the Hodge number . Varieties with have interesting properties, but are rather sparse, particularly in dimension . We discuss in this note a number of examples, in particular those constructed from curves with special Jacobians.
Radu Laza (2016)
Journal of the European Mathematical Society
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Inspired by the ideas of the minimal model program, Shepherd-Barron, Kollár, and Alexeev have constructed a geometric compactification for the moduli space of surfaces of log general type. In this paper, we discuss one of the simplest examples that fits into this framework: the case of pairs consisting of a degree two surface and an ample divisor . Specifically, we construct and describe explicitly a geometric compactification for the moduli of degree two pairs. This compactification...
Samuel Boissière, Alessandra Sarti (2007)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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This paper deals with surfaces with many lines. It is well-known that a cubic contains of them and that the maximal number for a quartic is . In higher degree the question remains open. Here we study classical and new constructions of surfaces with high number of lines. We obtain a symmetric octic with lines, and give examples of surfaces of degree containing a sequence of skew lines.
Gerd Dethloff, Pham Hoang Ha, Pham Duc Thoan (2016)
Colloquium Mathematicae
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We study the ramification of the Gauss map of complete minimal surfaces in on annular ends. This is a continuation of previous work of Dethloff-Ha (2014), which we extend here to targets of higher dimension.
Margarida Mendes Lopes, Rita Pardini (2008)
Journal of the European Mathematical Society
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We give explicit constructions of all the numerical Campedelli surfaces, i.e. the minimal surfaces of general type with and , whose fundamental group has order 9. There are three families, one with and two with . We also determine the base locus of the bicanonical system of these surfaces. It turns out that for the surfaces with and for one of the families of surfaces with the base locus consists of two points. To our knowlegde, these are the only known examples of surfaces...
Matthias Schütt, Andreas Schweizer (2013)
Annales de l’institut Fourier
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We explicitly determine the elliptic surfaces with section and maximal singular fibre. If the characteristic of the ground field is different from , for each of the two possible maximal fibre types, and , the surface is unique. In characteristic the maximal fibre types are and , and there exist two (resp. one) one-parameter families of such surfaces.
Fabrizio Catanese, Fabio Tonoli (2007)
Journal of the European Mathematical Society
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We determine the possible even sets of nodes on sextic surfaces in , showing in particular that their cardinalities are exactly the numbers in the set . We also show that all the possible cases admit an explicit description. The methods that we use are an interplay of coding theory and projective geometry on one hand, and of homological and computer algebra on the other. We give a detailed geometric construction for the new case of an even set of 56 nodes, but the ultimate verification...
Gerd Dethloff, Pham Hoang Ha (2014)
Annales de la faculté des sciences de Toulouse Mathématiques
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In this article, we study the ramification of the Gauss map of complete minimal surfaces in and on annular ends. We obtain results which are similar to the ones obtained by Fujimoto ([4], [5]) and Ru ([13], [14]) for (the whole) complete minimal surfaces, thus we show that the restriction of the Gauss map to an annular end of such a complete minimal surface cannot have more branching (and in particular not avoid more values) than on the whole complete minimal surface. We thus give...
Stefano Montaldo, Irene I. Onnis (2007)
Bollettino dell'Unione Matematica Italiana
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In this article we consider surfaces in the product space of the hyperbolic plane with the real line. The main results are: a description of some geometric properties of minimal graphs; new examples of complete minimal graphs; the local classification of totally umbilical surfaces.
Michał Stukow (2006)
Fundamenta Mathematicae
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Let be the Dehn twist about a circle a on an orientable surface. It is well known that for each circle b and an integer n, , where I(·,·) is the geometric intersection number. We prove a similar formula for circles on nonorientable surfaces. As a corollary we prove some algebraic properties of twists on nonorientable surfaces. We also prove that if ℳ(N) is the mapping class group of a nonorientable surface N, then up to a finite number of exceptions, the centraliser of the subgroup...
Florent Balacheff, Eran Makover, Hugo Parlier (2014)
Annales de la faculté des sciences de Toulouse Mathématiques
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In this note, we observe that the maximum value achieved by the systole function over all complete finite area hyperbolic surfaces of a given signature is greater than a function that grows logarithmically in terms of the ratio .
Bendehiba Senoussi, Hassan Al-Zoubi (2020)
Commentationes Mathematicae Universitatis Carolinae
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In the homogeneous space Sol, a translation surface is parametrized by , where and are curves contained in coordinate planes. In this article, we study translation invariant surfaces in , which has finite type immersion.
Víctor Jiménez López, Gabriel Soler López (2006)
Bollettino dell'Unione Matematica Italiana
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An explicit topological description of ω-limit sets of continuous flows on compact surfaces without boundary is given. Some of the results can be extended to manifolds of larger dimensions.
Ciro Ciliberto (1983)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Gilberto Bini, John Harer (2011)
Journal of the European Mathematical Society
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Let be the moduli space of -pointed Riemann surfaces of genus . Denote by the Deligne-Mumford compactification of . In the present paper, we calculate the orbifold and the ordinary Euler characteristic of for any and such that .
Carlos Matheus, Gabriela Weitze-Schmithüsen (2013)
Bulletin de la Société Mathématique de France
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We construct an explicit family of arithmetic Teichmüller curves , , supporting -invariant probabilities such that the associated -representation on has complementary series for every . Actually, the size of the spectral gap along this family goes to zero. In particular, the Teichmüller geodesic flow restricted to these explicit arithmetic Teichmüller curves has arbitrarily slow rate of exponential mixing.
Piotr Blass
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CONTENTSAcknowledgements...................................................................................................5Introduction..............................................................................................................6Notations..................................................................................................................8Chapter I. Zariski surfaces: definition and general properties................................10Chapter II. The theory...
Ralph M. Kaufmann (2009)
Banach Center Publications
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We define a new operad based on surfaces with foliations which contains suboperads. We construct CW models for these operads and provide applications of these models by giving actions on Hochschild complexes (thus making contact with string topology), by giving explicit cell representatives for the Dyer-Lashof-Cohen operations for the 2-cubes and by constructing new Ω spectra. The underlying novel principle is that we can trade genus in the surface representation vs. the dimension...
Daniel Allcock, James A. Carlson, Domingo Toledo (2010)
Annales scientifiques de l'École Normale Supérieure
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Let be the moduli space of smooth real cubic surfaces. We show that each of its components admits a real hyperbolic structure. More precisely, one can remove some lower-dimensional geodesic subspaces from a real hyperbolic space and form the quotient by an arithmetic group to obtain an orbifold isomorphic to a component of the moduli space. There are five components. For each we describe the corresponding lattices in . We also derive several new and several old results on the topology...