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Author: Mircea Mustaţă
Publisher: American Mathematical Soc.
ISBN: 1470437813
Category : Education
Languages : en
Pages : 92
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Book Description
The authors use methods from birational geometry to study the Hodge filtration on the localization along a hypersurface. This filtration leads to a sequence of ideal sheaves, called Hodge ideals, the first of which is a multiplier ideal. They analyze their local and global properties, and use them for applications related to the singularities and Hodge theory of hypersurfaces and their complements.
Author: Mircea Mustaţă
Publisher: American Mathematical Soc.
ISBN: 1470437813
Category : Education
Languages : en
Pages : 92
Get Book Here
Book Description
The authors use methods from birational geometry to study the Hodge filtration on the localization along a hypersurface. This filtration leads to a sequence of ideal sheaves, called Hodge ideals, the first of which is a multiplier ideal. They analyze their local and global properties, and use them for applications related to the singularities and Hodge theory of hypersurfaces and their complements.
Author: Boyan Sirakov
Publisher: World Scientific
ISBN: 9813272899
Category : Mathematics
Languages : en
Pages : 5393
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Book Description
The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.
Author: Spencer Bloch
Publisher: Springer
ISBN: 3540383883
Category : Mathematics
Languages : en
Pages : 313
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Book Description
Author: Claire Voisin
Publisher: Cambridge University Press
ISBN: 9780521718011
Category : Mathematics
Languages : en
Pages : 334
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Book Description
This is a modern introduction to Kaehlerian geometry and Hodge structure. Coverage begins with variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory (with the latter being treated in a more theoretical way than is usual in geometry). The book culminates with the Hodge decomposition theorem. In between, the author proves the Kaehler identities, which leads to the hard Lefschetz theorem and the Hodge index theorem. The second part of the book investigates the meaning of these results in several directions.
Author: Jaroslav Nešetřil
Publisher: American Mathematical Soc.
ISBN: 1470440652
Category : Education
Languages : en
Pages : 120
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Book Description
In this paper the authors introduce a general framework for the study of limits of relational structures and graphs in particular, which is based on a combination of model theory and (functional) analysis. The authors show how the various approaches to graph limits fit to this framework and that the authors naturally appear as “tractable cases” of a general theory. As an outcome of this, the authors provide extensions of known results. The authors believe that this puts these into a broader context. The second part of the paper is devoted to the study of sparse structures. First, the authors consider limits of structures with bounded diameter connected components and prove that in this case the convergence can be “almost” studied component-wise. They also propose the structure of limit objects for convergent sequences of sparse structures. Eventually, they consider the specific case of limits of colored rooted trees with bounded height and of graphs with bounded tree-depth, motivated by their role as “elementary bricks” these graphs play in decompositions of sparse graphs, and give an explicit construction of a limit object in this case. This limit object is a graph built on a standard probability space with the property that every first-order definable set of tuples is measurable. This is an example of the general concept of modeling the authors introduce here. Their example is also the first “intermediate class” with explicitly defined limit structures where the inverse problem has been solved.
Author: S. V. Ivanov
Publisher: American Mathematical Soc.
ISBN: 1470441438
Category : Education
Languages : en
Pages : 118
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Book Description
The author introduces and studies the bounded word problem and the precise word problem for groups given by means of generators and defining relations. For example, for every finitely presented group, the bounded word problem is in NP, i.e., it can be solved in nondeterministic polynomial time, and the precise word problem is in PSPACE, i.e., it can be solved in polynomial space. The main technical result of the paper states that, for certain finite presentations of groups, which include the Baumslag-Solitar one-relator groups and free products of cyclic groups, the bounded word problem and the precise word problem can be solved in polylogarithmic space. As consequences of developed techniques that can be described as calculus of brackets, the author obtains polylogarithmic space bounds for the computational complexity of the diagram problem for free groups, for the width problem for elements of free groups, and for computation of the area defined by polygonal singular closed curves in the plane. The author also obtains polynomial time bounds for these problems.
Author: Bruno Anglès
Publisher: Springer Nature
ISBN: 3030662497
Category : Mathematics
Languages : en
Pages : 337
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Book Description
This volume introduces some recent developments in Arithmetic Geometry over local fields. Its seven chapters are centered around two common themes: the study of Drinfeld modules and non-Archimedean analytic geometry. The notes grew out of lectures held during the research program "Arithmetic and geometry of local and global fields" which took place at the Vietnam Institute of Advanced Study in Mathematics (VIASM) from June to August 2018. The authors, leading experts in the field, have put great effort into making the text as self-contained as possible, introducing the basic tools of the subject. The numerous concrete examples and suggested research problems will enable graduate students and young researchers to quickly reach the frontiers of this fascinating branch of mathematics.
Author: Andrew J. Blumberg
Publisher: American Mathematical Soc.
ISBN: 1470441780
Category : Mathematics
Languages : en
Pages : 112
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Book Description
The authors resolve the longstanding confusion about localization sequences in $THH$ and $TC$ and establish a specialized devissage theorem.
Author: Victor Beresnevich
Publisher: American Mathematical Soc.
ISBN: 1470440954
Category : Education
Languages : en
Pages : 92
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Book Description
Author: Antonio Alarcón
Publisher: American Mathematical Soc.
ISBN: 1470441616
Category : Education
Languages : en
Pages : 90
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Book Description
All the new tools mentioned above apply to non-orientable minimal surfaces endowed with a fixed choice of a conformal structure. This enables the authors to obtain significant new applications to the global theory of non-orientable minimal surfaces. In particular, they construct proper non-orientable conformal minimal surfaces in Rn with any given conformal structure, complete non-orientable minimal surfaces in Rn with arbitrary conformal type whose generalized Gauss map is nondegenerate and omits n hyperplanes of CPn−1 in general position, complete non-orientable minimal surfaces bounded by Jordan curves, and complete proper non-orientable minimal surfaces normalized by bordered surfaces in p-convex domains of Rn.
