An Introduction to Families, Deformations and Moduli - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Introduction to Families, Deformations and Moduli write by Thiruvalloor E. Venkata Balaji. This book was released on 2010. An Introduction to Families, Deformations and Moduli available in PDF, EPUB and Kindle. Moduli Theory is one of those areas of Mathematics that has fascinated minds from classical to modern times. This has been so because it reveals beautiful Geometry naturally hidden in questions involving classification of geometric objects and because of the profound use of the methods of several areas of Mathematics like Algebra, Number Theory, Topology and Analysis to achieve this revelation. A study of Moduli Theory would therefore give senior undergraduate and graduate students an integrated view of Mathematics. The present book is a humble introduction to some aspects of Moduli Theory.
The Moduli Space of Curves
The Moduli Space of Curves - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Moduli Space of Curves write by Robert H. Dijkgraaf. This book was released on 2012-12-06. The Moduli Space of Curves available in PDF, EPUB and Kindle. The moduli space Mg of curves of fixed genus g – that is, the algebraic variety that parametrizes all curves of genus g – is one of the most intriguing objects of study in algebraic geometry these days. Its appeal results not only from its beautiful mathematical structure but also from recent developments in theoretical physics, in particular in conformal field theory.
Lie Methods in Deformation Theory
Lie Methods in Deformation Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lie Methods in Deformation Theory write by Marco Manetti. This book was released on 2022-08-01. Lie Methods in Deformation Theory available in PDF, EPUB and Kindle. This book furnishes a comprehensive treatment of differential graded Lie algebras, L-infinity algebras, and their use in deformation theory. We believe it is the first textbook devoted to this subject, although the first chapters are also covered in other sources with a different perspective. Deformation theory is an important subject in algebra and algebraic geometry, with an origin that dates back to Kodaira, Spencer, Kuranishi, Gerstenhaber, and Grothendieck. In the last 30 years, a new approach, based on ideas from rational homotopy theory, has made it possible not only to solve long-standing open problems, but also to clarify the general theory and to relate apparently different features. This approach works over a field of characteristic 0, and the central role is played by the notions of differential graded Lie algebra, L-infinity algebra, and Maurer–Cartan equations. The book is written keeping in mind graduate students with a basic knowledge of homological algebra and complex algebraic geometry as utilized, for instance, in the book by K. Kodaira, Complex Manifolds and Deformation of Complex Structures. Although the main applications in this book concern deformation theory of complex manifolds, vector bundles, and holomorphic maps, the underlying algebraic theory also applies to a wider class of deformation problems, and it is a prerequisite for anyone interested in derived deformation theory. Researchers in algebra, algebraic geometry, algebraic topology, deformation theory, and noncommutative geometry are the major targets for the book.
Moduli of Curves
Moduli of Curves - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Moduli of Curves write by Joe Harris. This book was released on 2006-04-06. Moduli of Curves available in PDF, EPUB and Kindle. A guide to a rich and fascinating subject: algebraic curves and how they vary in families. Providing a broad but compact overview of the field, this book is accessible to readers with a modest background in algebraic geometry. It develops many techniques, including Hilbert schemes, deformation theory, stable reduction, intersection theory, and geometric invariant theory, with the focus on examples and applications arising in the study of moduli of curves. From such foundations, the book goes on to show how moduli spaces of curves are constructed, illustrates typical applications with the proofs of the Brill-Noether and Gieseker-Petri theorems via limit linear series, and surveys the most important results about their geometry ranging from irreducibility and complete subvarieties to ample divisors and Kodaira dimension. With over 180 exercises and 70 figures, the book also provides a concise introduction to the main results and open problems about important topics which are not covered in detail.
The Geometry of Moduli Spaces of Sheaves
The Geometry of Moduli Spaces of Sheaves - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Geometry of Moduli Spaces of Sheaves write by Daniel Huybrechts. This book was released on 2010-05-27. The Geometry of Moduli Spaces of Sheaves available in PDF, EPUB and Kindle. This edition has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces. The authors review changes in the field and point the reader towards further literature. An ideal text for graduate students or mathematicians with a background in algebraic geometry.
