perfect complex
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Author(s):  
Kwokwai Chan ◽  
Ziming Nikolas Ma

Abstract We apply the techniques developed in [2] to study smoothings of a pair $(X,\mathfrak{C}^*)$, where $\mathfrak{C}^*$ is a bounded perfect complex of locally free sheaves over a degenerate Calabi–Yau variety $X$. In particular, if $X$ is a projective Calabi–Yau variety admitting the structure of a toroidal crossing space and with the higher tangent sheaf $\mathcal{T}^1_X$ globally generated, and $\mathfrak{F}$ is a locally free sheaf over $X$, then we prove, using the results in [ 8], that the pair $(X,\mathfrak{F})$ is formally smoothable when $\textrm{Ext}^2(\mathfrak{F},\mathfrak{F})_0 = 0$ and $H^2(X,\mathcal{O}_X) = 0$.


Author(s):  
Олег Омеличкин ◽  
Oleg Omelichkin

<p>The paper deals with the matters of structure and functions of political culture, which present a holistic system that consists of various levels and constituents linked by feedback and co-subordination relations. Culture is a composition of specific ideal content (the meaning-generating elements) and form (structure, practical implementation), which are inseparable from each other. Their correlation can be represented as the interaction of the ideal and the real models of political culture. The author identifies a variety of elements in its structure, including political language, standard value system, models of political participation, etc. All these constituents are interrelated and coordinated, and their combinations form a particular configuration of culture. They make a perfect complex which contains a general programme of political legacy and development of the society. The social mission of political culture is manifested in its functions (identification, integration, socialization, etc.) which help reproduce the current governance system and implement new political projects and decisions.</p>


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