The Moduli Space of Cubic Threefolds as a Ball Quotient
Author: Daniel Allcock
Publisher: American Mathematical Soc.
Published: 2011
Total Pages: 89
ISBN-13: 0821847511
DOWNLOAD EBOOK"Volume 209, number 985 (fourth of 5 numbers)."
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Cohomology of the Moduli Space of Cubic Threefolds and Its Smooth Models
Author: Sebastian Casalaina-Martin
Publisher: American Mathematical Society
Published: 2023-02-13
Total Pages: 112
ISBN-13: 1470460203
DOWNLOAD EBOOKView the abstract.
Current Developments in Algebraic Geometry
Author: Lucia Caporaso
Publisher: Cambridge University Press
Published: 2012-03-19
Total Pages: 437
ISBN-13: 052176825X
DOWNLOAD EBOOKThis volume, based on a workshop by the MSRI, offers an overview of the state of the art in many areas of algebraic geometry.
Compact Moduli Spaces and Vector Bundles
Author: Valery Alexeev
Publisher: American Mathematical Soc.
Published: 2012
Total Pages: 264
ISBN-13: 0821868993
DOWNLOAD EBOOKThis book contains the proceedings of the conference on Compact Moduli and Vector Bundles, held from October 21-24, 2010, at the University of Georgia. This book is a mix of survey papers and original research articles on two related subjects: Compact Moduli spaces of algebraic varieties, including of higher-dimensional stable varieties and pairs, and Vector Bundles on such compact moduli spaces, including the conformal block bundles. These bundles originated in the 1970s in physics; the celebrated Verlinde formula computes their ranks. Among the surveys are those that examine compact moduli spaces of surfaces of general type and others that concern the GIT constructions of log canonical models of moduli of stable curves. The original research articles include, among others, papers on a formula for the Chern classes of conformal classes of conformal block bundles on the moduli spaces of stable curves, on Looijenga's conjectures, on algebraic and tropical Brill-Noether theory, on Green's conjecture, on rigid curves on moduli of curves, and on Steiner surfaces.
Compactifying Moduli Spaces
Author: Paul Hacking
Publisher: Birkhäuser
Published: 2016-02-04
Total Pages: 141
ISBN-13: 3034809212
DOWNLOAD EBOOKThis 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.
The Geometry of Cubic Hypersurfaces
Author: Daniel Huybrechts
Publisher: Cambridge University Press
Published: 2023-06-30
Total Pages: 462
ISBN-13: 1009279998
DOWNLOAD EBOOKCubic hypersurfaces are described by almost the simplest possible polynomial equations, yet their behaviour is rich enough to demonstrate many of the central challenges in algebraic geometry. With exercises and detailed references to the wider literature, this thorough text introduces cubic hypersurfaces and all the techniques needed to study them. The book starts by laying the foundations for the study of cubic hypersurfaces and of many other algebraic varieties, covering cohomology and Hodge theory of hypersurfaces, moduli spaces of those and Fano varieties of linear subspaces contained in hypersurfaces. The next three chapters examine the general machinery applied to cubic hypersurfaces of dimension two, three, and four. Finally, the author looks at cubic hypersurfaces from a categorical point of view and describes motivic features. Based on the author's lecture courses, this is an ideal text for graduate students as well as an invaluable reference for researchers in algebraic geometry.
Geometry of Riemann Surfaces
Author: William J. Harvey
Publisher: Cambridge University Press
Published: 2010-02-11
Total Pages: 416
ISBN-13: 0521733073
DOWNLOAD EBOOKOriginal research and expert surveys on Riemann surfaces.
Birational Geometry and Moduli Spaces
Author: Elisabetta Colombo
Publisher: Springer Nature
Published: 2020-02-25
Total Pages: 204
ISBN-13: 303037114X
DOWNLOAD EBOOKThis volume collects contributions from speakers at the INdAM Workshop “Birational Geometry and Moduli Spaces”, which was held in Rome on 11–15 June 2018. The workshop was devoted to the interplay between birational geometry and moduli spaces and the contributions of the volume reflect the same idea, focusing on both these areas and their interaction. In particular, the book includes both surveys and original papers on irreducible holomorphic symplectic manifolds, Severi varieties, degenerations of Calabi-Yau varieties, uniruled threefolds, toric Fano threefolds, mirror symmetry, canonical bundle formula, the Lefschetz principle, birational transformations, and deformations of diagrams of algebras. The intention is to disseminate the knowledge of advanced results and key techniques used to solve open problems. The book is intended for all advanced graduate students and researchers interested in the new research frontiers of birational geometry and moduli spaces.
A Celebration of Algebraic Geometry
Author: Brendan Hassett
Publisher: American Mathematical Soc.
Published: 2013-09-11
Total Pages: 614
ISBN-13: 0821889834
DOWNLOAD EBOOKThis volume resulted from the conference A Celebration of Algebraic Geometry, which was held at Harvard University from August 25-28, 2011, in honor of Joe Harris' 60th birthday. Harris is famous around the world for his lively textbooks and enthusiastic teaching, as well as for his seminal research contributions. The articles are written in this spirit: clear, original, engaging, enlivened by examples, and accessible to young mathematicians. The articles in this volume focus on the moduli space of curves and more general varieties, commutative algebra, invariant theory, enumerative geometry both classical and modern, rationally connected and Fano varieties, Hodge theory and abelian varieties, and Calabi-Yau and hyperkähler manifolds. Taken together, they present a comprehensive view of the long frontier of current knowledge in algebraic geometry. Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).
Algebraic Geometry
Author: Igor V. Dolgachev
Publisher: American Mathematical Soc.
Published: 2007
Total Pages: 256
ISBN-13: 0821842013
DOWNLOAD EBOOKThis volume contains the proceedings of the Korea-Japan Conference on Algebraic Geometry in honor of Igor Dolgachev on his sixtieth birthday. The articles in this volume explore a wide variety of problems that illustrate interactions between algebraic geometry and other branches of mathematics. Among the topics covered by this volume are algebraic curve theory, algebraic surface theory, moduli space, automorphic forms, Mordell-Weil lattices, and automorphisms of hyperkahler manifolds. This book is an excellent and rich reference source for researchers.
