Displaying similar documents to “Numerical Campedelli surfaces with fundamental group of order 9”

Counting lines on surfaces

Samuel Boissière, Alessandra Sarti (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

This paper deals with surfaces with many lines. It is well-known that a cubic contains 27 of them and that the maximal number for a quartic is 64 . 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 352 lines, and give examples of surfaces of degree d containing a sequence of d ( d - 2 ) + 4 skew lines.

The KSBA compactification for the moduli space of degree two K 3 pairs

Radu Laza (2016)

Journal of the European Mathematical Society

Similarity:

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 ( X , H ) consisting of a degree two K 3 surface X and an ample divisor H . Specifically, we construct and describe explicitly a geometric compactification P ¯ 2 for the moduli of degree two K 3 pairs. This compactification...

Even sets of nodes on sextic surfaces

Fabrizio Catanese, Fabio Tonoli (2007)

Journal of the European Mathematical Society

Similarity:

We determine the possible even sets of nodes on sextic surfaces in 3 , showing in particular that their cardinalities are exactly the numbers in the set { 24 , 32 , 40 , 56 } . 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...

Some surfaces with maximal Picard number

Arnaud Beauville (2014)

Journal de l’École polytechnique — Mathématiques

Similarity:

For a smooth complex projective variety, the rank ρ of the Néron-Severi group is bounded by the Hodge number h 1 , 1 . Varieties with ρ = h 1 , 1 have interesting properties, but are rather sparse, particularly in dimension 2 . We discuss in this note a number of examples, in particular those constructed from curves with special Jacobians.

Higgs bundles and representation spaces associated to morphisms

Indranil Biswas, Carlos Florentino (2015)

Archivum Mathematicum

Similarity:

Let G be a connected reductive affine algebraic group defined over the complex numbers, and K G be a maximal compact subgroup. Let X , Y be irreducible smooth complex projective varieties and f : X Y an algebraic morphism, such that π 1 ( Y ) is virtually nilpotent and the homomorphism f * : π 1 ( X ) π 1 ( Y ) is surjective. Define f ( π 1 ( X ) , G ) = { ρ Hom ( π 1 ( X ) , G ) A ρ factors through f * } , f ( π 1 ( X ) , K ) = { ρ Hom ( π 1 ( X ) , K ) A ρ factors through f * } , where A : G GL ( Lie ( G ) ) is the adjoint action. We prove that the geometric invariant theoretic quotient f ( π 1 ( X , x 0 ) , G ) / / G admits a deformation retraction to f ( π 1 ( X , x 0 ) , K ) / K . We also show that the space of conjugacy classes of n almost commuting...

Persistence of Coron’s solution in nearly critical problems

Monica Musso, Angela Pistoia (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

We consider the problem - Δ u = u N + 2 N - 2 + λ in Ω ε ω , u > 0 in Ω ε ω , u = 0 on Ω ε ω , where Ω and ω are smooth bounded domains in N , N 3 , ε > 0 and λ . We prove that if the size of the hole ε goes to zero and if, simultaneously, the parameter λ goes to zero at the appropriate rate, then the problem has a solution which blows up at the origin.

Natural pseudodistances between closed surfaces

Pietro Donatini, Patrizio Frosini (2007)

Journal of the European Mathematical Society

Similarity:

Let us consider two closed surfaces , 𝒩 of class C 1 and two functions ϕ : , ψ : 𝒩 of class C 1 , called measuring functions. The natural pseudodistance d between the pairs ( , ) , ( 𝒩 , ψ ) is defined as the infimum of Θ ( f ) : = max P | ϕ ( P ) ψ ( f ( P ) ) | as f varies in the set of all homeomorphisms from onto 𝒩 . In this paper we prove that the natural pseudodistance equals either | c 1 c 2 | , 1 2 | c 1 c 2 | , or 1 3 | c 1 c 2 | , where c 1 and c 2 are two suitable critical values of the measuring functions. This shows that a previous relation between the natural pseudodistance and...

Sobolev versus Hölder local minimizers and existence of multiple solutions for a singular quasilinear equation

Jacques Giacomoni, Ian Schindler, Peter Takáč (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

We investigate the following quasilinear and singular problem, t o 2 . 7 c m - Δ p u = λ u δ + u q in Ω ; u | Ω = 0 , u > 0 in Ω , t o 2 . 7 c m (P) where Ω is an open bounded domain with smooth boundary, 1 < p < , p - 1 < q p * - 1 , λ > 0 , and 0 < δ < 1 . As usual, p * = N p N - p if 1 < p < N , p * ( p , ) is arbitrarily large if p = N , and p * = if p > N . We employ variational methods in order to show the existence of at least two distinct (positive) solutions of problem (P) in W 0 1 , p ( Ω ) . While following an approach due to Ambrosetti-Brezis-Cerami, we need to prove two new results of separate interest: a strong comparison principle...

On the uniqueness of elliptic K3 surfaces with maximal singular fibre

Matthias Schütt, Andreas Schweizer (2013)

Annales de l’institut Fourier

Similarity:

We explicitly determine the elliptic K 3 surfaces with section and maximal singular fibre. If the characteristic of the ground field is different from 2 , for each of the two possible maximal fibre types, I 19 and I 14 * , the surface is unique. In characteristic 2 the maximal fibre types are I 18 and I 13 * , and there exist two (resp. one) one-parameter families of such surfaces.

Explicit cogenerators for the homotopy category of projective modules over a ring

Amnon Neeman (2011)

Annales scientifiques de l'École Normale Supérieure

Similarity:

Let R be a ring. In two previous articles [12, 14] we studied the homotopy category 𝐊 ( R - Proj ) of projective R -modules. We produced a set of generators for this category, proved that the category is 1 -compactly generated for any ring R , and showed that it need not always be compactly generated, but is for sufficiently nice R . We furthermore analyzed the inclusion j ! : 𝐊 ( R - Proj ) 𝐊 ( R - Flat ) and the orthogonal subcategory 𝒮 = 𝐊 ( R - Proj ) . And we even showed that the inclusion 𝒮 𝐊 ( R - Flat ) has a right adjoint; this forces some natural map to be...

On surfaces with p 𝑔 = q = 1 and non-ruled bicanonical involution

Carlos Rito (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

This paper classifies surfaces S of general type with p g = q = 1 having an involution i such that S / i has non-negative Kodaira dimension and that the bicanonical map of S factors through the double cover induced by i . It is shown that S / i is regular and either: a) the Albanese fibration of S is of genus 2 or b) S has no genus 2 fibration and S / i is birational to a K 3 surface. For case a) a list of possibilities and examples are given. An example for case b) with K 2 = 6 is also constructed.

Subclasses of typically real functions determined by some modular inequalities

Leopold Koczan, Katarzyna Trąbka-Więcław (2010)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

Similarity:

Let T be the family of all typically real functions, i.e. functions that are analytic in the unit disk Δ : = { z : | z | < 1 } , normalized by f ( 0 ) = f ' ( 0 ) - 1 = 0 and such that Im z Im f ( z ) 0 for z Δ . Moreover, let us denote: T ( 2 ) : = { f T : f ( z ) = - f ( - z ) for z Δ } and T M , g : = { f T : f M g in Δ } , where M > 1 , g T S and S consists of all analytic functions, normalized and univalent in Δ .We investigate  classes in which the subordination is replaced with the majorization and the function g is typically real but does not necessarily univalent, i.e. classes { f T : f M g in Δ } , where M > 1 , g T , which we denote...

Green's generic syzygy conjecture for curves of even genus lying on a K3 surface

Claire Voisin (2002)

Journal of the European Mathematical Society

Similarity:

We consider the generic Green conjecture on syzygies of a canonical curve, and particularly the following reformulation thereof: For a smooth projective curve C of genus g in characteristic 0, the condition Cliff C > l is equivalent to the fact that K g - l ' - 2 , 1 ( C , K C ) = 0 , l ' l . We propose a new approach, which allows up to prove this result for generic curves C of genus g ( C ) and gonality gon(C) in the range g ( C ) 3 + 1 gon(C) g ( C ) 2 + 1 .

Noncommutative del Pezzo surfaces and Calabi-Yau algebras

Pavel Etingof, Victor Ginzburg (2010)

Journal of the European Mathematical Society

Similarity:

The hypersurface in 3 with an isolated quasi-homogeneous elliptic singularity of type E ˜ r , r = 6 , 7 , 8 , has a natural Poisson structure. We show that the family of del Pezzo surfaces of the corresponding type E r provides a semiuniversal Poisson deformation of that Poisson structure. We also construct a deformation-quantization of the coordinate ring of such a del Pezzo surface. To this end, we first deform the polynomial algebra [ x 1 , x 2 , x 3 ] to a noncommutative algebra with generators x 1 , x 2 , x 3 and the following 3 relations...

Sufficient Conditions for Integrability of Distortion Function Kf 1

Costantino Capozzoli (2009)

Bollettino dell'Unione Matematica Italiana

Similarity:

Assume that Ω , Ω are planar domains and f : Ω onto Ω is a homeomorphism belonging to Sobolev space W loc 1 , 1 ( Ω ; 2 ) with finite distortion. We prove that if the distortion function K f of f satisfies the condition dist EXP ( K f , L ) < 1 , then the distortion function K f - 1 of f - 1 belongs to L loc 1 ( Ω ) . We show that this result is sharp in sense that the conclusion fails if dist EXP ( K f , L ) = 1 . Moreover, we prove that if the distortion function K f satisfies the condition dist EXP ( K f , L ) = λ for some λ > 0 , then K f - 1 belongs to L loc p ( Ω ) for every p ( 0 , 1 2 λ ) . As special case of this result we show that if...

On the Anderson-Badawi ω R [ X ] ( I [ X ] ) = ω R ( I ) conjecture

Peyman Nasehpour (2016)

Archivum Mathematicum

Similarity:

Let R be a commutative ring with an identity different from zero and n be a positive integer. Anderson and Badawi, in their paper on n -absorbing ideals, define a proper ideal I of a commutative ring R to be an n -absorbing ideal of R , if whenever x 1 x n + 1 I for x 1 , ... , x n + 1 R , then there are n of the x i ’s whose product is in I and conjecture that ω R [ X ] ( I [ X ] ) = ω R ( I ) for any ideal I of an arbitrary ring R , where ω R ( I ) = min { n : I is an n -absorbing ideal of R } . In the present paper, we use content formula techniques to prove that their conjecture is true, if one of the following...