Modifications of complex varieties and the Chow Lemma

1974 ◽  
pp. 133-139
Author(s):  
Boris Moishezon
Keyword(s):  
Complex Varieties

scholarly journals Strong submeasures and applications to non-compact dynamical systems

2020 ◽  
pp. 1-23
Author(s):  
TUYEN TRUNG TRUONG
Keyword(s):  
Metric Space ◽  
Bounded Operator ◽  
Continuous Functions ◽  
Open Dense Subset ◽  
Compact Metric Space ◽  
Basic Properties ◽  
Banach Theorem ◽  
Complex Varieties ◽  
Definition Of ◽  
Meromorphic Maps

Abstract A strong submeasure on a compact metric space X is a sub-linear and bounded operator on the space of continuous functions on X. A strong submeasure is positive if it is non-decreasing. By the Hahn–Banach theorem, a positive strong submeasure is the supremum of a non-empty collection of measures whose masses are uniformly bounded from above. There are many natural examples of continuous maps of the form $f:U\rightarrow X$ , where X is a compact metric space and $U\subset X$ is an open-dense subset, where f cannot extend to a reasonable function on X. We can mention cases such as transcendental maps of $\mathbb {C}$ , meromorphic maps on compact complex varieties, or continuous self-maps $f:U\rightarrow U$ of a dense open subset $U\subset X$ where X is a compact metric space. For the aforementioned mentioned the use of measures is not sufficient to establish the basic properties of ergodic theory, such as the existence of invariant measures or a reasonable definition of measure-theoretic entropy and topological entropy. In this paper we show that strong submeasures can be used to completely resolve the issue and establish these basic properties. In another paper we apply strong submeasures to the intersection of positive closed $(1,1)$ currents on compact Kähler manifolds.

scholarly journals Comparing K -theories for complex varieties

2001 ◽  
Vol 123 (5) ◽  
pp. 779-810 ◽  
Author(s):  
Eric M. Friedlander ◽  
Mark E. Walker
Keyword(s):  
Complex Varieties

scholarly journals Arithmeticity of the monodromy of some Kodaira fibrations

2019 ◽  
Vol 156 (1) ◽  
pp. 114-157
Author(s):  
Nick Salter ◽  
Bena Tshishiku
Keyword(s):  
Mapping Class Group ◽  
Class Group ◽  
Monodromy Group ◽  
Algebraic Curves ◽  
Algebraic Surfaces ◽  
Mapping Class ◽  
Complex Varieties

A question of Griffiths–Schmid asks when the monodromy group of an algebraic family of complex varieties is arithmetic. We resolve this in the affirmative for a class of algebraic surfaces known as Atiyah–Kodaira manifolds, which have base and fibers equal to complete algebraic curves. Our methods are topological in nature and involve an analysis of the ‘geometric’ monodromy, valued in the mapping class group of the fiber.

scholarly journals Approximation of plurisubharmonic functions on complex varieties

2017 ◽  
Vol 28 (14) ◽  
pp. 1750107
Author(s):  
Nguyen Quang Dieu ◽  
Tang Van Long ◽  
Sanphet Ounheuan
Keyword(s):  
Continuous Function ◽  
Bounded Domain ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Plurisubharmonic Functions ◽  
Complex Variety ◽  
Complex Varieties

Let [Formula: see text] be a complex variety in a bounded domain [Formula: see text] in [Formula: see text]. We are interested in finding sufficient conditions on [Formula: see text] so that plurisubharmonic functions which are bounded from above on [Formula: see text] can be approximated from above by continuous functions on [Formula: see text] and plurisubharmonic on [Formula: see text] Next, we discuss the possibility to extend a given real valued continuous function on [Formula: see text] to a maximal plurisubharmonic on [Formula: see text] which is continuous up to the boundary.

Multiple final embedding of clauses

2010 ◽  
Vol 15 (1) ◽  
pp. 88-105 ◽  
Author(s):  
Fred Karlsson
Keyword(s):  
Language Processing ◽  
Relative Clauses ◽  
Language Use ◽  
Main Clause ◽  
Ancient Greek ◽  
Successive Level ◽  
Complex Varieties ◽  
Corpus Data ◽  
Processing Mechanisms

There are no grammatical limits on multiple final embedding of clauses. But converging corpus data from English, Finnish, German and Swedish show that multiple final embedding is avoided at levels deeper than three levels from the main clause in syntactically simple varieties, and at levels deeper than five levels in complex varieties. The frequency of every successive level of final embedding decreases by a factor of seven down to levels 4–5. Only relative clauses allow free self-embedding, within the limits just mentioned. These restrictions are regularities of language use, stylistic preferences related to the properties of various types of discourse. Ultimately they are explained by cognitive and other properties of the language processing mechanisms. The frequencies of final embedding depths in modern languages such as English and Finnish is not accidental. Ancient Greek had reached this profile by 300 BC, suggesting cross-linguistic generality of the preferences.

Continuation of Complex Varieties Across Rectifiable Sets

1995 ◽  
Vol 47 (4) ◽  
pp. 877-896
Author(s):  
Yeren Xu
Keyword(s):  
Finite Length ◽  
Dimensional Case ◽  
Exceptional Set ◽  
Complex Varieties ◽  
Rectifiable Sets

AbstractWe continue our research on extension of complex varieties across closed subsets. While efforts are being made to deal with varieties of any dimensions, the paper primarily concerns 1-dimensional case, and the exceptional set is thus assumed to be connected with finite length. As applications of the main result, several corollaries are obtained with interesting features.

Homological Planes in the Grothendieck Ring of Varieties

2015 ◽  
Vol 58 (2) ◽  
pp. 356-362
Author(s):  
Julien Sebag
Keyword(s):  
Algebraic Surface ◽  
Grothendieck Group ◽  
Grothendieck Ring ◽  
Complex Varieties ◽  
Smooth Affine

AbstractIn this note we identify the classes of Q-homological planes in the Grothendieck group of complex varieties K0(VarC). Precisely, we prove that a connected, smooth, affine, complex, algebraic surface X is a Q-homological plane if and only if [X] = in the ring K0(VarC) and Pic(X)Q := Pic(X) ⊗z Q = 0.

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