β Scribed by Brambila-Paz L., Newstead P., Thomas R.P.W., Garcia-Prada O. (eds.)
No coin nor oath required. For personal study only.
Moduli theory is the study of how objects, typically in algebraic geometry but sometimes in other areas of mathematics, vary in families and is fundamental to an understanding of the objects themselves. First formalised in the 1960s, it represents a significant topic of modern mathematical research with strong connections to many areas of mathematics (including geometry, topology and number theory) and other disciplines such as theoretical physics. This book, which arose from a programme at the Isaac Newton Institute in Cambridge, is an ideal way for graduate students and more experienced researchers to become acquainted with the wealth of ideas and problems in moduli theory and related areas. The reader will find articles on both fundamental material and cutting-edge research topics, such as: algebraic stacks; BPS states and the P = W conjecture; stability conditions; derived differential geometry; and counting curves in algebraic varieties, all written by leading experts
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Spaces of particles have long been studied in homotopy theory, partly for their intrinsic interest but also for their role in describing the structure of loop spaces. Recently the structure of these spaces has been put to good use in understanding several moduli spaces of solutions to variational pr
<p>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.</p> <p>Three contributions give an insight on particular aspects of moduli problems. In the first of them, various ways to constru
<p><p>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.</p><p>Three contributions give an insight on particular aspects of moduli problems. In the first of them, various ways to const
Vector bundles and their associated moduli spaces are of fundamental importance in algebraic geometry. In recent decades this subject has been greatly enhanced by its relationships with other areas of mathematics, including differential geometry, topology and even theoretical physics, specifically g
Vector bundles and their associated moduli spaces are of fundamental importance in algebraic geometry. In recent decades this subject has been greatly enhanced by its relationships with other areas of mathematics, including differential geometry, topology and even theoretical physics, specifically g