scholarly journals Manin’s conjecture and the Fujita invariant of finite covers

2021 ◽  
Vol 15 (8) ◽  
pp. 2071-2087
Author(s):  
Akash Kumar Sengupta
Keyword(s):  
Finite Covers ◽  
Manin’S Conjecture

scholarly journals Permutation groups with small orbit growth

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Manuel Bodirsky ◽  
Bertalan Bodor
Keyword(s):  
Automorphism Group ◽  
Constraint Satisfaction ◽  
Constraint Satisfaction Problem ◽  
Permutation Groups ◽  
First Order ◽  
Finite Covers

Abstract Let K exp + \mathcal{K}_{{\operatorname{exp}}{+}} be the class of all structures 𝔄 such that the automorphism group of 𝔄 has at most c ⁢ n d ⁢ n cn^{dn} orbits in its componentwise action on the set of 𝑛-tuples with pairwise distinct entries, for some constants c , d c,d with d < 1 d<1 . We show that K exp + \mathcal{K}_{{\operatorname{exp}}{+}} is precisely the class of finite covers of first-order reducts of unary structures, and also that K exp + \mathcal{K}_{{\operatorname{exp}}{+}} is precisely the class of first-order reducts of finite covers of unary structures. It follows that the class of first-order reducts of finite covers of unary structures is closed under taking model companions and model-complete cores, which is an important property when studying the constraint satisfaction problem for structures from K exp + \mathcal{K}_{{\operatorname{exp}}{+}} . We also show that Thomas’ conjecture holds for K exp + \mathcal{K}_{{\operatorname{exp}}{+}} : all structures in K exp + \mathcal{K}_{{\operatorname{exp}}{+}} have finitely many first-order reducts up to first-order interdefinability.

scholarly journals Manin’s conjecture for quartic Del Pezzo surfaces with a conic fibration

2011 ◽  
Vol 160 (1) ◽  
pp. 1-69 ◽  
Author(s):  
R. De la Bretèche ◽  
T. D. Browning
Keyword(s):  
Del Pezzo Surfaces ◽  
Del Pezzo ◽  
Manin’S Conjecture

scholarly journals Constructing 1-cusped isospectral non-isometric hyperbolic 3-manifolds

2017 ◽  
Vol 10 (01) ◽  
pp. 1-25
Author(s):  
Stavros Garoufalidis ◽  
Alan W. Reid
Keyword(s):  
Discrete Spectrum ◽  
Eisenstein Series ◽  
Finite Volume ◽  
Finite Covers ◽  
Figure Eight Knot ◽  
Complex Length

We construct infinitely many examples of pairs of isospectral but non-isometric [Formula: see text]-cusped hyperbolic [Formula: see text]-manifolds. These examples have infinite discrete spectrum and the same Eisenstein series. Our constructions are based on an application of Sunada’s method in the cusped setting, and so in addition our pairs are finite covers of the same degree of a 1-cusped hyperbolic 3-orbifold (indeed manifold) and also have the same complex length spectra. Finally we prove that any finite volume hyperbolic 3-manifold isospectral to the figure-eight knot complement is homeomorphic to the figure-eight knot complement.

Finite Covers of 3-Manifolds Containing Essential Tori

1988 ◽  
Vol 310 (1) ◽  
pp. 381 ◽  
Author(s):  
John Luecke
Keyword(s):  
Finite Covers

scholarly journals Deformation of finite morphisms and smoothing of ropes

2008 ◽  
Vol 144 (3) ◽  
pp. 673-688 ◽  
Author(s):  
Francisco Javier Gallego ◽  
Miguel González ◽  
Bangere P. Purnaprajna
Keyword(s):  
General Theory ◽  
Projective Space ◽  
General Result ◽  
The Other ◽  
Independent Interest ◽  
Higher Dimension ◽  
Smooth Curves ◽  
Other Hand ◽  
Finite Covers ◽  
The One

AbstractIn this paper we prove that most ropes of arbitrary multiplicity supported on smooth curves can be smoothed. By a rope being smoothable we mean that the rope is the flat limit of a family of smooth, irreducible curves. To construct a smoothing, we connect, on the one hand, deformations of a finite morphism to projective space and, on the other hand, morphisms from a rope to projective space. We also prove a general result of independent interest, namely that finite covers onto smooth irreducible curves embedded in projective space can be deformed to a family of 1:1 maps. We apply our general theory to prove the smoothing of ropes of multiplicity 3 on P1. Even though this paper focuses on ropes of dimension 1, our method yields a general approach to deal with the smoothing of ropes of higher dimension.

scholarly journals La conjecture de Manin pour une famille de variétés en dimension supérieure

2018 ◽  
Vol 166 (3) ◽  
pp. 433-486 ◽  
Author(s):  
KEVIN DESTAGNOL
Keyword(s):  
Infinite Family ◽  
Strong Form ◽  
Higher Dimension ◽  
Crepant Resolution ◽  
Projective Varieties ◽  
Formula Group ◽  
Image Position ◽  
Manin’S Conjecture

AbstractInspired by a method of La Bretèche relying on some unique factorisation, we generalise work of Blomer, Brüdern and Salberger to prove Manin's conjecture in its strong form conjectured by Peyre for some infinite family of varieties of higher dimension. The varieties under consideration in this paper correspond to the singular projective varieties defined by the following equation$$ x_1 y_2y_3\cdots y_n+x_2y_1y_3 \cdots y_n+ \cdots+x_n y_1 y_2 \cdots y_{n-1}=0 $$in ℙℚ2n−1for alln⩾ 3. This paper comes with an Appendix by Per Salberger constructing a crepant resolution of the above varieties.

scholarly journals Nori fundamental gerbe of essentially finite covers and Galois closure of towers of torsors

2019 ◽  
Vol 25 (2) ◽  
Author(s):  
Marco Antei ◽  
Indranil Biswas ◽  
Michel Emsalem ◽  
Fabio Tonini ◽  
Lei Zhang
Keyword(s):  
Galois Closure ◽  
Finite Covers

scholarly journals Second cohomology groups and finite covers of infinite symmetric groups

2011 ◽  
Vol 330 (1) ◽  
pp. 221-233 ◽  
Author(s):  
David M. Evans ◽  
Elisabetta Pastori
Keyword(s):  
Symmetric Groups ◽  
Cohomology Groups ◽  
Finite Covers
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