Articles or demands made by the Kings most Excellent Majestie to the gentry and commonalty of the county of Salop [[electronic resource] ] : on Saturday the 8. of October. 1642. With an exact answer to every particular therein presented to His Majesty at Shrewesbury the same day, by the high sheriffe of the said county. Wherein is exactly manifested, how active the malignant party of this kingdome are to incense the King against the Parliament, and to engage him in a destructive warre against his subjects

• Record Nr.: UNISA996392803003316
• Pubbl/distr/stampa: London, : Printed for Henry Hutton, Octob. 12. 1642
• Descrizione fisica: [8] p
• Soggetti: Great Britain History Civil War, 1642-1649 Early works to 1800; Salop (England) History Early works to 1800
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: A news pamphlet incorporating the texts of the king's proclamation and a reply from the citizens of Shropshire.; With a title-page woodcut of the royal arms.; Signatures: A⁴.; Reproduction of the original in the British Library.
• Sommario/riassunto: eebo-0018

Algebraic Curves : Towards Moduli Spaces / / by Maxim E. Kazaryan, Sergei K. Lando, Victor V. Prasolov

• Record Nr.: UNINA9910309661403321
• Autore: Kazaryan Maxim E
• Pubbl/distr/stampa: Cham : , : Springer International Publishing : , : Imprint : Springer, , 2018
• ISBN: 9783030029432; 3030029433
• Edizione: [1st ed. 2018.]
• Descrizione fisica: 1 online resource (XIV, 231 p. 37 illus.)
• Collana: Moscow Lectures, , 2522-0314 ; ; 2
• Disciplina: 516.352
• Soggetti: Geometry, Algebraic; Functions of complex variables; Mathematical physics; Algebraic Geometry; Functions of a Complex Variable; Mathematical Physics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Introduction -- 1 Preliminaries – 2 Algebraic curves -- 3 Complex structure and the topology of curves -- 4 Curves in projective spaces -- 5 Plücker formulas -- 6 Mappings of curves -- 7 Differential 1-forms on curves -- 8 Line bundles, linear systems, and divisors -- 9 Riemann–Roch formula and its applications -- 10 Proof of the Riemann–Roch formula -- 11 Weierstrass points -- 12 Abel’s theorem -- 13 Examples of moduli spaces -- 14 Approaches to constructing moduli spaces -- 15 Moduli spaces of rational curves with marked points -- 16 Stable curves -- 17 A backward look from the viewpoint of characteristic classes -- 18 Moduli spaces of stable maps -- 19 Exam problems -- References -- Index.
• Sommario/riassunto: This book offers a concise yet thorough introduction to the notion of moduli spaces of complex algebraic curves. Over the last few decades, this notion has become central not only in algebraic geometry, but in mathematical physics, including string theory, as well. The book begins by studying individual smooth algebraic curves, including the most ; beautiful ones, before addressing families of curves. Studying families of algebraic curves often proves to be more efficient than studying individual curves: these families and their total spaces can still be smooth, even if there are singular curves among their members. A major discovery of the 20th century, attributed to P. Deligne and D. Mumford, was that curves with only mild singularities form smooth compact moduli spaces. An unexpected byproduct of this discovery was the realization that the analysis of more complex curve singularities is not a necessary step in understanding the geometry of the moduli spaces. The book does not use the sophisticated machinery of modern algebraic geometry, and most classical objects related to curves – such as Jacobian, space of holomorphic differentials, the Riemann-Roch theorem, and Weierstrass points – are treated at a basic level that does not require a profound command of algebraic geometry, but which is sufficient for extending them to vector bundles and other geometric objects associated to moduli spaces. Nevertheless, it offers clear information on the construction of the moduli spaces, and provides readers with tools for practical operations with this notion. Based on several lecture courses given by the authors at the Independent University of Moscow and Higher School of Economics, the book also includes a wealth of problems, making it suitable not only for individual research, but also as a textbook for undergraduate and graduate coursework.