Displaying similar documents to “Noncommutative del Pezzo surfaces and Calabi-Yau algebras”

Cluster ensembles, quantization and the dilogarithm

Vladimir V. Fock, Alexander B. Goncharov (2009)

Annales scientifiques de l'École Normale Supérieure

Similarity:

A cluster ensemble is a pair ( 𝒳 , 𝒜 ) of positive spaces (i.e. varieties equipped with positive atlases), coming with an action of a symmetry group Γ . The space 𝒜 is closely related to the spectrum of a cluster algebra [12]. The two spaces are related by a morphism p : 𝒜 𝒳 . The space 𝒜 is equipped with a closed 2 -form, possibly degenerate, and the space 𝒳 has a Poisson structure. The map p is compatible with these structures. The dilogarithm together with its motivic and quantum avatars plays a central...

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.

Poisson geometry and deformation quantization near a strictly pseudoconvex boundary

Eric Leichtnam, Xiang Tang, Alan Weinstein (2007)

Journal of the European Mathematical Society

Similarity:

Let X be a complex manifold with strongly pseudoconvex boundary M . If ψ is a defining function for M , then log ψ is plurisubharmonic on a neighborhood of M in X , and the (real) 2-form σ = i ¯ ( log ψ ) is a symplectic structure on the complement of M in a neighborhood of M in X ; it blows up along M . The Poisson structure obtained by inverting σ extends smoothly across M and determines a contact structure on M which is the same as the one induced by the complex structure. When M is compact, the Poisson structure...

On the Picard number of divisors in Fano manifolds

Cinzia Casagrande (2012)

Annales scientifiques de l'École Normale Supérieure

Similarity:

Let  X be a complex Fano manifold of arbitrary dimension, and D a prime divisor in  X . We consider the image 𝒩 1 ( D , X ) of  𝒩 1 ( D ) in  𝒩 1 ( X ) under the natural push-forward of 1 -cycles. We show that ρ X - ρ D codim 𝒩 1 ( D , X ) 8 . Moreover if codim 𝒩 1 ( D , X ) 3 , then either X S × T where S is a Del Pezzo surface, or codim 𝒩 1 ( D , X ) = 3 and X has a fibration in Del Pezzo surfaces onto a Fano manifold T such that ρ X - ρ T = 4 .

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...

Prolongation of Poisson 2 -form on Weil bundles

Norbert Mahoungou Moukala, Basile Guy Richard Bossoto (2016)

Archivum Mathematicum

Similarity:

In this paper, M denotes a smooth manifold of dimension n , A a Weil algebra and M A the associated Weil bundle. When ( M , ω M ) is a Poisson manifold with 2 -form ω M , we construct the 2 -Poisson form ω M A A , prolongation on M A of the 2 -Poisson form ω M . We give a necessary and sufficient condition for that M A be an A -Poisson manifold.

Augmentation quotients for Burnside rings of generalized dihedral groups

Shan Chang (2016)

Czechoslovak Mathematical Journal

Similarity:

Let H be a finite abelian group of odd order, 𝒟 be its generalized dihedral group, i.e., the semidirect product of C 2 acting on H by inverting elements, where C 2 is the cyclic group of order two. Let Ω ( 𝒟 ) be the Burnside ring of 𝒟 , Δ ( 𝒟 ) be the augmentation ideal of Ω ( 𝒟 ) . Denote by Δ n ( 𝒟 ) and Q n ( 𝒟 ) the n th power of Δ ( 𝒟 ) and the n th consecutive quotient group Δ n ( 𝒟 ) / Δ n + 1 ( 𝒟 ) , respectively. This paper provides an explicit -basis for Δ n ( 𝒟 ) and determines the isomorphism class of Q n ( 𝒟 ) for each positive integer n .

Sum-product theorems and incidence geometry

Mei-Chu Chang, Jozsef Solymosi (2007)

Journal of the European Mathematical Society

Similarity:

In this paper we prove the following theorems in incidence geometry. 1. There is δ > 0 such that for any P 1 , , P 4 , and Q 1 , , Q n 2 , if there are n ( 1 + δ ) / 2 many distinct lines between P i and Q j for all i , j , then P 1 , , P 4 are collinear. If the number of the distinct lines is < c n 1 / 2 then the cross ratio of the four points is algebraic. 2. Given c > 0 , there is δ > 0 such that for any P 1 , P 2 , P 3 2 noncollinear, and Q 1 , , Q n 2 , if there are c n 1 / 2 many distinct lines between P i and Q j for all i , j , then for any P 2 { P 1 , P 2 , P 3 } , we have δ n distinct lines between P and Q j . 3. Given...

𝒞 k -regularity for the ¯ -equation with a support condition

Shaban Khidr, Osama Abdelkader (2017)

Czechoslovak Mathematical Journal

Similarity:

Let D be a 𝒞 d q -convex intersection, d 2 , 0 q n - 1 , in a complex manifold X of complex dimension n , n 2 , and let E be a holomorphic vector bundle of rank N over X . In this paper, 𝒞 k -estimates, k = 2 , 3 , , , for solutions to the ¯ -equation with small loss of smoothness are obtained for E -valued ( 0 , s ) -forms on D when n - q s n . In addition, we solve the ¯ -equation with a support condition in 𝒞 k -spaces. More precisely, we prove that for a ¯ -closed form f in 𝒞 0 , q k ( X D , E ) , 1 q n - 2 , n 3 , with compact support and for ε with 0 < ε < 1 there...

Complex series and connected sets

B. Jasek

Similarity:

CONTENTSPREFACE..........................................................................................................................................................................3INTRODUCTION............................................................................................................................................................. 41. Notation. 2. Subject of the paper.Chapter I. DECOMPOSITION OF Σ INTO Σ 1 , Σ 2 , Σ 3 , Σ 4 INESSENTIAL RESTRICTIONOF GENERALITY ...............................................................................................................................................................