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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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.
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.
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.
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...
Ciro Ciliberto (1983)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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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...
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.
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...
Gerard van der Geer, T. Katsura (2000)
Journal of the European Mathematical Society
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In this paper we give a characterization of the height of K3 surfaces in characteristic . This enables us to calculate the cycle classes in families of K3 surfaces of the loci where the height is at least . The formulas for such loci can be seen as generalizations of the famous formula of Deuring for the number of supersingular elliptic curves in characteristic . In order to describe the tangent spaces to these loci we study the first cohomology of higher closed forms.
Thierry De Pauw (2009)
Annales scientifiques de l'École Normale Supérieure
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We prove a new existence theorem pertaining to the Plateau problem in -dimensional Euclidean space. We compare the approach of E.R. Reifenberg with that of H. Federer and W.H. Fleming. A relevant technical step consists in showing that compact rectifiable surfaces are approximatable in Hausdorff measure and in Hausdorff distance by locally acyclic surfaces having the same boundary.
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 .
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...
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.
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...
В.Ю. Ровенский (1989)
Sibirskij matematiceskij zurnal
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Sachiko Hamano (2014)
Annales Polonici Mathematici
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We show the variation formula for the Schiffer span s(t) for moving Riemann surfaces R(t) with , and apply it to show the simultaneous uniformization of moving planar Riemann surfaces of class .
K. K. Dube (1974)
Matematički Vesnik
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Zbigniew Duszyński (2007)
Bollettino dell'Unione Matematica Italiana
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Corresponding to [27], some properties of S-closed subspaces and subsets -closed relative to a topological space are proved. Conditions under which mappings preserve certain -closed subspaces are investigated.