Classifying Spaces of Degenerating Polarized Hodge Structures. (AM-169) PDF Download
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Author: Kazuya Kato
Publisher: Princeton University Press
ISBN: 0691138222
Category : Mathematics
Languages : en
Pages : 349
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Book Description
In 1970, Phillip Griffiths envisioned that points at infinity could be added to the classifying space D of polarized Hodge structures. In this book, Kazuya Kato and Sampei Usui realize this dream by creating a logarithmic Hodge theory. They use the logarithmic structures begun by Fontaine-Illusie to revive nilpotent orbits as a logarithmic Hodge structure. The book focuses on two principal topics. First, Kato and Usui construct the fine moduli space of polarized logarithmic Hodge structures with additional structures. Even for a Hermitian symmetric domain D, the present theory is a refinement of the toroidal compactifications by Mumford et al. For general D, fine moduli spaces may have slits caused by Griffiths transversality at the boundary and be no longer locally compact. Second, Kato and Usui construct eight enlargements of D and describe their relations by a fundamental diagram, where four of these enlargements live in the Hodge theoretic area and the other four live in the algebra-group theoretic area. These two areas are connected by a continuous map given by the SL(2)-orbit theorem of Cattani-Kaplan-Schmid. This diagram is used for the construction in the first topic.
Author: Kazuya Kato
Publisher: Princeton University Press
ISBN: 0691138222
Category : Mathematics
Languages : en
Pages : 349
Get Book Here
Book Description
In 1970, Phillip Griffiths envisioned that points at infinity could be added to the classifying space D of polarized Hodge structures. In this book, Kazuya Kato and Sampei Usui realize this dream by creating a logarithmic Hodge theory. They use the logarithmic structures begun by Fontaine-Illusie to revive nilpotent orbits as a logarithmic Hodge structure. The book focuses on two principal topics. First, Kato and Usui construct the fine moduli space of polarized logarithmic Hodge structures with additional structures. Even for a Hermitian symmetric domain D, the present theory is a refinement of the toroidal compactifications by Mumford et al. For general D, fine moduli spaces may have slits caused by Griffiths transversality at the boundary and be no longer locally compact. Second, Kato and Usui construct eight enlargements of D and describe their relations by a fundamental diagram, where four of these enlargements live in the Hodge theoretic area and the other four live in the algebra-group theoretic area. These two areas are connected by a continuous map given by the SL(2)-orbit theorem of Cattani-Kaplan-Schmid. This diagram is used for the construction in the first topic.
Author: Matt Kerr
Publisher: Cambridge University Press
ISBN: 1316531392
Category : Mathematics
Languages : en
Pages : 533
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Book Description
In its simplest form, Hodge theory is the study of periods – integrals of algebraic differential forms which arise in the study of complex geometry and moduli, number theory and physics. Organized around the basic concepts of variations of Hodge structure and period maps, this volume draws together new developments in deformation theory, mirror symmetry, Galois representations, iterated integrals, algebraic cycles and the Hodge conjecture. Its mixture of high-quality expository and research articles make it a useful resource for graduate students and seasoned researchers alike.
Author: Paola Comparin
Publisher: American Mathematical Soc.
ISBN: 1470453274
Category : Education
Languages : en
Pages : 294
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Book Description
Articles in this volume are based on lectures given at three conferences on Geometry at the Frontier, held at the Universidad de la Frontera, Pucón, Chile in 2016, 2017, and 2018. The papers cover recent developments on the theory of algebraic varieties—in particular, of their automorphism groups and moduli spaces. They will be of interest to anyone working in the area, as well as young mathematicians and students interested in complex and algebraic geometry.
Author: Jan Nagel
Publisher: Cambridge University Press
ISBN: 0521701740
Category : Mathematics
Languages : en
Pages : 293
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Book Description
This 2007 book is a self-contained account of the subject of algebraic cycles and motives.
Author: Valery Alexeev
Publisher: American Mathematical Soc.
ISBN: 0821843346
Category : Mathematics
Languages : en
Pages : 290
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Book Description
"This book is devoted to recent progress in the study of curves and abelian varieties. It discusses both classical aspects of this deep and beautiful subject as well as two important new developments, tropical geometry and the theory of log schemes." "In addition to original research articles, this book contains three surveys devoted to singularities of theta divisors. of compactified Jucobiuns of singular curves, and of "strange duality" among moduli spaces of vector bundles on algebraic varieties."--BOOK JACKET.
Author: Phillip A Griffiths
Publisher: World Scientific
ISBN: 9814476846
Category : Mathematics
Languages : en
Pages : 532
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Book Description
Shiing-Shen Chern (1911-2004) was one of the leading differential geometers of the twentieth century. In 1946, he founded the Mathematical Institute of Academia Sinica in Shanghai, which was later moved to Nanking. In 1981, he founded the Mathematical Sciences Research Institute (MSRI) at Berkeley and acted as the director until 1984. In 1985, he founded the Nankai Institute of Mathematics in Tianjin. He was awarded the National Medal of Science in 1975; the Wolf Prize in mathematics in 1984; and the Shaw Prize in mathematical sciences in 2004.Chern's works span all the classic fields of differential geometry: the Chern-Simons theory; the Chern-Weil theory, linking curvature invariants to characteristic classes; Chern classes; and other areas such as projective differential geometry and webs that are mathematically rich but currently have a lower profile. He also published work in integral geometry, value distribution theory of holomorphic functions, and minimal submanifolds.Inspired by Chern and his work, former colleagues, students and friends — themselves highly regarded mathematicians in their own right — come together to honor and celebrate Chern's huge contributions. The volume, organized by Phillip Griffiths of the Institute for Advanced Study (Princeton), contains contributions by Michael Atiyah (University of Edinburgh), C-M Bai (Nankai), Robert Bryant (Duke University), Kung-Ching Chang (Peking University), Jeff Cheeger (New York University), Simon K Donaldson (Imperial College), Hélène Esnault (Universität Duisburg-Essen), Mo-Lin Ge (Nankai), Mark Green (University of California at Los Angeles), Phillip Griffiths (Institute for Advanced Study), F Reese Harvey (Rice University), Alain Hénaut (Université Bordeaux 1), Niky Kamran (McGill University), Bruce Kleiner (Yale), H Blaine Lawson, Jr (Suny at Stony Brook), Yiming Long (Nankai), Xiaonan Ma (UMR 7640 du CNRS), Luc Pirio (IRMAR, France), Graeme Segal (Oxford), Gang Tian (MIT), Jean-Marie Trepreau (Institut de Mathématiques de Jussieu), Jeff Viaclovsky (MIT), Wei Wang (Nankai), Wentsun Wu (Chinese Academy of Sciences), C N Yang (Tsinghua), Tan Zhang (Murray State University), Weiping Zhang (Nankai) and others.
Author: Bruce Hunt
Publisher: Springer Nature
ISBN: 3030698041
Category : Mathematics
Languages : en
Pages : 637
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Book Description
What do the classification of algebraic surfaces, Weyl's dimension formula and maximal orders in central simple algebras have in common? All are related to a type of manifold called locally mixed symmetric spaces in this book. The presentation emphasizes geometric concepts and relations and gives each reader the "roter Faden", starting from the basics and proceeding towards quite advanced topics which lie at the intersection of differential and algebraic geometry, algebra and topology. Avoiding technicalities and assuming only a working knowledge of real Lie groups, the text provides a wealth of examples of symmetric spaces. The last two chapters deal with one particular case (Kuga fiber spaces) and a generalization (elliptic surfaces), both of which require some knowledge of algebraic geometry. Of interest to topologists, differential or algebraic geometers working in areas related to arithmetic groups, the book also offers an introduction to the ideas for non-experts.
Author: Paul Hacking
Publisher: Birkhäuser
ISBN: 3034809212
Category : Mathematics
Languages : en
Pages : 141
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Book Description
This book focusses on a large class of objects in moduli theory and provides different perspectives from which compactifications of moduli spaces may be investigated. Three contributions give an insight on particular aspects of moduli problems. In the first of them, various ways to construct and compactify moduli spaces are presented. In the second, some questions on the boundary of moduli spaces of surfaces are addressed. Finally, the theory of stable quotients is explained, which yields meaningful compactifications of moduli spaces of maps. Both advanced graduate students and researchers in algebraic geometry will find this book a valuable read.
Author: David Loeffler
Publisher: Springer
ISBN: 3319450328
Category : Mathematics
Languages : en
Pages : 494
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Book Description
Celebrating one of the leading figures in contemporary number theory – John H. Coates – on the occasion of his 70th birthday, this collection of contributions covers a range of topics in number theory, concentrating on the arithmetic of elliptic curves, modular forms, and Galois representations. Several of the contributions in this volume were presented at the conference Elliptic Curves, Modular Forms and Iwasawa Theory, held in honour of the 70th birthday of John Coates in Cambridge, March 25-27, 2015. The main unifying theme is Iwasawa theory, a field that John Coates himself has done much to create. This collection is indispensable reading for researchers in Iwasawa theory, and is interesting and valuable for those in many related fields.
Author: Jacob Lurie
Publisher: Princeton University Press
ISBN: 9780691140490
Category : Mathematics
Languages : en
Pages : 948
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Book Description
In 'Higher Topos Theory', Jacob Lurie presents the foundations of this theory using the language of weak Kan complexes introduced by Boardman and Vogt, and shows how existing theorems in algebraic topology can be reformulated and generalized in the theory's new language.
