scholarly journals ERRATUM/CORRIGENDUM, OCTOBER 2020, FOR ’A BOGOMOLOV UNOBSTRUCTEDNESS THEOREM FOR LOG-SYMPLECTIC MANIFOLDS IN GENERAL POSITION’ (J. INST. MATH. JUSSIEU 19 (2018), 1509–1519)

Author(s):  
Ziv Ran

Abstract The general position hypothesis needs strengthening.

2018 ◽  
Vol 19 (5) ◽  
pp. 1509-1519
Author(s):  
Ziv Ran

We consider compact Kählerian manifolds $X$ of even dimension 4 or more, endowed with a log-symplectic holomorphic Poisson structure $\unicode[STIX]{x1D6F1}$ which is sufficiently general, in a precise linear sense, with respect to its (normal-crossing) degeneracy divisor $D(\unicode[STIX]{x1D6F1})$. We prove that $(X,\unicode[STIX]{x1D6F1})$ has unobstructed deformations, that the tangent space to its deformation space can be identified in terms of the mixed Hodge structure on $H^{2}$ of the open symplectic manifold $X\setminus D(\unicode[STIX]{x1D6F1})$, and in fact coincides with this $H^{2}$ provided the Hodge number $h_{X}^{2,0}=0$, and finally that the degeneracy locus $D(\unicode[STIX]{x1D6F1})$ deforms locally trivially under deformations of $(X,\unicode[STIX]{x1D6F1})$.


Author(s):  
Dusa McDuff ◽  
Dietmar Salamon

This chapter examines various ways to construct symplectic manifolds and submanifolds. It begins by studying blowing up and down in both the complex and the symplectic contexts. The next section is devoted to a discussion of fibre connected sums and describes Gompf’s construction of symplectic four-manifolds with arbitrary fundamental group. The chapter also contains an exposition of Gromov’s telescope construction, which shows that for open manifolds the h-principle rules and the inclusion of the space of symplectic forms into the space of nondegenerate 2-forms is a homotopy equivalence. The final section outlines Donaldson’s construction of codimension two symplectic submanifolds and explains the associated decompositions of the ambient manifold.


2021 ◽  
Vol 62 (3) ◽  
pp. 033506
Author(s):  
Oğul Esen ◽  
Manuel de León ◽  
Cristina Sardón ◽  
Marcin Zajşc

2021 ◽  
pp. 147309522110011
Author(s):  
Esin Özdemir

In this article, I readdress the issue of rationality, which has been so far considered in western liberal democracies and in planning theory as procedural, and more recently as post-political in the post-foundational approach, aiming to show how it can gain a substantive and politicising character. I first discuss the problems and limits of the treatment of rational thinking as well as rational consensus-seeking as merely procedural and post-political. Secondly, utilising the notion of Realrationalität of Flyvbjerg, I discuss how rationality attains a politicising role due to its strong relationship with power. Using the concept of planning rationality aiming at public interest, I present the general position and actions of professional organisations in Turkey, focusing on the Chamber of City Planners, as an example illustrative of my argument. I finally argue that rationality becomes a substantive issue that politicizes planning, when it is put forward as an alternative to authoritarian market logic. In doing so, I adopt the Rancièrian definition of the political, defined as disclosure of a wrong and staging of equality. In conclusion, I first emphasize the importance of avoiding quick rejections of the concepts of rationality and consensus in the framework of planning activity and planning theory and secondly, call for a broader definition of the political; the political that is not confined to conflict but is open to rational thinking and rational consensus.


Author(s):  
JING TIAN ◽  
KEXIANG XU ◽  
SANDI KLAVŽAR

Abstract The general position number of a connected graph is the cardinality of a largest set of vertices such that no three pairwise-distinct vertices from the set lie on a common shortest path. In this paper it is proved that the general position number is additive on the Cartesian product of two trees.


2021 ◽  
Vol 62 (3) ◽  
pp. 033513
Author(s):  
Panagiotis Batakidis ◽  
Ramón Vera

2020 ◽  
pp. 1-25
Author(s):  
CHIARA CAMERE ◽  
ALBERTO CATTANEO ◽  
ANDREA CATTANEO

We study irreducible holomorphic symplectic manifolds deformation equivalent to Hilbert schemes of points on a $K3$ surface and admitting a non-symplectic involution. We classify the possible discriminant quadratic forms of the invariant and coinvariant lattice for the action of the involution on cohomology and explicitly describe the lattices in the cases where the invariant lattice has small rank. We also give a modular description of all $d$ -dimensional families of manifolds of $K3^{[n]}$ -type with a non-symplectic involution for $d\geqslant 19$ and $n\leqslant 5$ and provide examples arising as moduli spaces of twisted sheaves on a $K3$ surface.


1999 ◽  
Vol 128 (1) ◽  
pp. 237-243 ◽  
Author(s):  
Mark J. Gotay ◽  
Janusz Grabowski ◽  
Hendrik B. Grundling
Keyword(s):  

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