scholarly journals The Slope of Surfaces with Albanese Dimension One

2018 ◽  
Vol 167 (02) ◽  
pp. 355-360
Author(s):  
STEFANO VIDUSSI
Keyword(s):  
Fundamental Group ◽  
General Type ◽  
Cyclic Covers ◽  
Dimension One ◽  
Dense Set ◽  
Double Coverings

AbstractMendes Lopes and Pardini showed that minimal general type surfaces of Albanese dimension one have slopes K2/χ dense in the interval [2,8]. This result was completed to cover the admissible interval [2,9] by Roulleau and Urzua, who proved that surfaces with fundamental group equal to that of any curve of genus g ≥ 1 (in particular, having Albanese dimension one) give a set of slopes dense in [6,9]. In this note we provide a second construction that complements that of Mendes Lopes–Pardini, to recast a dense set of slopes in [8,9] for surfaces of Albanese dimension one. These surfaces arise as ramified double coverings of cyclic covers of the Cartwright–Steger surface.

scholarly journals NEW EXAMPLES OF CALABI–YAU 3-FOLDS AND GENUS ZERO SURFACES

2014 ◽  
Vol 16 (02) ◽  
pp. 1350010 ◽  
Author(s):  
GILBERTO BINI ◽  
FILIPPO F. FAVALE ◽  
JORGE NEVES ◽  
ROBERTO PIGNATELLI
Keyword(s):  
Fundamental Group ◽  
Moduli Space ◽  
General Type ◽  
Picard Number ◽  
Surfaces Of General Type ◽  
Geometric Genus ◽  
Genus Zero ◽  
New Family ◽  
Hodge Numbers ◽  
Projective Lines

We classify the subgroups of the automorphism group of the product of four projective lines admitting an invariant anticanonical smooth divisor on which the action is free. As a first application, we describe new examples of Calabi–Yau 3-folds with small Hodge numbers. In particular, the Picard number is 1 and the number of moduli is 5. Furthermore, the fundamental group is nontrivial. We also construct a new family of minimal surfaces of general type with geometric genus zero, K2 = 3 and fundamental group of order 16. We show that this family dominates an irreducible component of dimension 4 of the moduli space of the surfaces of general type.

scholarly journals ALBANESE VARIETIES OF CYCLIC COVERS OF THE PROJECTIVE PLANE AND ORBIFOLD PENCILS

2016 ◽  
Vol 227 ◽  
pp. 189-213
Author(s):  
E. ARTAL BARTOLO ◽  
J. I. COGOLLUDO-AGUSTÍN ◽  
A. LIBGOBER
Keyword(s):  
Projective Plane ◽  
Fundamental Group ◽  
Sufficient Conditions ◽  
Main Tool ◽  
Plane Curves ◽  
Abelian Surface ◽  
Singular Curve ◽  
Cyclic Covers ◽  
Genus 2 ◽  
Multiple Fibers

The paper studies a relation between fundamental group of the complement to a plane singular curve and the orbifold pencils containing it. The main tool is the use of Albanese varieties of cyclic covers ramified along such curves. Our results give sufficient conditions for a plane singular curve to belong to an orbifold pencil, that is, a pencil of plane curves with multiple fibers inducing a map onto an orbifold curve whose orbifold fundamental group is nontrivial. We construct an example of a cyclic cover of the projective plane which is an abelian surface isomorphic to the Jacobian of a curve of genus 2 illustrating the extent to which these conditions are necessary.

scholarly journals A Type-2 Fuzzy Sonewhere Dense Set In General Type-2 Fuzzy Topological Space

2020 ◽  
pp. 21-27
Author(s):  
Mohammed Salih Mahdy Hussan ◽  
Munir Abdul Khalik AL-Khafaji
Keyword(s):  
Topological Space ◽  
Fuzzy Set ◽  
General Type ◽  
Space Topology ◽  
Fuzzy Topological Space ◽  
Dense Set

The multiplicity of connotations in any paper does not mean that there is no main objective for that paper and certainly one of these papers is our research the main objective is to introduce a new connotation which is type-2 fuzzy somewhere dense set in general type-2 fuzzy topological space and its relationship with open sets of the connotation type-2 fuzzy set in the same space topology and theories of this connotation.

scholarly journals Some bidouble planes with pg = q = 0 and 4 ≤ K2 ≤ 7

2015 ◽  
Vol 26 (05) ◽  
pp. 1550035 ◽  
Author(s):  
Carlos Rito
Keyword(s):  
General Type ◽  
Enriques Surface ◽  
Surfaces Of General Type ◽  
Bicanonical Map ◽  
Double Coverings

We give a list of possibilities for surfaces of general type with pg = 0 having an involution i such that the bicanonical map of S is not composed with i and S/i is not rational. Some examples with K2 = 4, …, 7 are constructed as double coverings of an Enriques surface. These surfaces have a description as bidouble coverings of the plane.

scholarly journals Holomorphic affine connections on non-Kähler manifolds

2016 ◽  
Vol 27 (11) ◽  
pp. 1650094 ◽  
Author(s):  
Indranil Biswas ◽  
Sorin Dumitrescu
Keyword(s):  
Fundamental Group ◽  
Geometric Structure ◽  
Riemannian Metric ◽  
Complex Manifolds ◽  
Geometric Structures ◽  
Holomorphic Affine ◽  
Locally Homogeneous ◽  
Dimension One ◽  
Affine Type ◽  
Compact Complex Manifolds

Our aim here is to investigate the holomorphic geometric structures on compact complex manifolds which may not be Kähler. We prove that holomorphic geometric structures of affine type on compact Calabi–Yau manifolds with polystable tangent bundle (with respect to some Gauduchon metric on it) are locally homogeneous. In particular, if the geometric structure is rigid in Gromov’s sense, then the fundamental group of the manifold must be infinite. We also prove that compact complex manifolds of algebraic dimension one bearing a holomorphic Riemannian metric must have infinite fundamental group.

scholarly journals Incidence coefficients in the Novikov Complex for Morse forms: rationality and exponential growth properties

2021 ◽  
Vol 13 (4) ◽  
pp. 125-177
Author(s):  
Andrei Pajitnov
Keyword(s):  
Fundamental Group ◽  
Exponential Growth ◽  
Laurent Polynomials ◽  
Growth Properties ◽  
Boundary Operators ◽  
Morse Form ◽  
Homology Module ◽  
Dense Set ◽  
Refined Version ◽  
Novikov Complex

Let f : M → S 1 be a Morse map, v a transverse f -gradient. Theconstruction of the Novikov complex associates to these data a free chain complexC ∗ (f, v) over the ring Z[t]][t −1 ], generated by the critical points of f and computingthe completed homology module of the corresponding infinite cyclic covering of M .Novikov’s Exponential Growth Conjecture says that the boundary operators in thiscomplex are power series of non-zero convergence raduis.In [12] the author announced the proof of the Novikov conjecture for the case ofC 0 -generic gradients together with several generalizations. The proofs of the firstpart of this work were published in [13]. The present article contains the proofs ofthe second part.There is a refined version of the Novikov complex, defined over a suitable com-pletion of the group ring of the fundamental group. We prove that for a C 0 -genericf -gradient the corresponding incidence coefficients belong to the image in the Novikovring of a (non commutative) localization of the fundamental group ring.The Novikov construction generalizes also to the case of Morse 1-forms. In thiscase the corresponding incidence coefiicients belong to a certain completion of thering of integral Laurent polynomials of several variables. We prove that for a givenMorse form ω and a C 0 -generic ω-gradient these incidence coefficients are rationalfunctions.The incidence coefficients in the Novikov complex are obtained by counting thealgebraic number of the trajectories of the gradient, joining the zeros of the Morseform. There is V.I.Arnold’s version of the exponential growth conjecture, whichconcerns the total number of trajectories. We confirm this stronger form of theconjecture for any given Morse form and a C 0 -dense set of its gradients.We give an example of explicit computation of the Novikov complex.

scholarly journals Nonspecial varieties and generalised Lang–Vojta conjectures

2021 ◽  
Vol 9 ◽  
Author(s):  
Erwan Rousseau ◽  
Amos Turchet ◽  
Julie Tzu-Yueh Wang
Keyword(s):  
Number Field ◽  
Function Field ◽  
General Type ◽  
Function Fields ◽  
Rational Points ◽  
Special Variety ◽  
Recent Method ◽  
Dense Set

Abstract We construct a family of fibred threefolds $X_m \to (S , \Delta )$ such that $X_m$ has no étale cover that dominates a variety of general type but it dominates the orbifold $(S,\Delta )$ of general type. Following Campana, the threefolds $X_m$ are called weakly special but not special. The Weak Specialness Conjecture predicts that a weakly special variety defined over a number field has a potentially dense set of rational points. We prove that if m is big enough, the threefolds $X_m$ present behaviours that contradict the function field and analytic analogue of the Weak Specialness Conjecture. We prove our results by adapting the recent method of Ru and Vojta. We also formulate some generalisations of known conjectures on exceptional loci that fit into Campana’s program and prove some cases over function fields.

Sign in / Sign up

Export Citation Format

Share Document