Algebraic Curves Towards Moduli Spaces /

• Κύριοι συγγραφείς: Kazaryan, Maxim E. (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut), Lando, Sergei K. (http://id.loc.gov/vocabulary/relators/aut), Prasolov, Victor V. (http://id.loc.gov/vocabulary/relators/aut)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Έκδοση: 1st ed. 2018.
• Σειρά: Moscow Lectures, 2
• Θέματα: Algebraic geometry.; Functions of complex variables.; Mathematical physics.; Algebraic Geometry.; Functions of a Complex Variable.; Mathematical Physics.

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 indivi...

Πίνακας περιεχομένων:

• 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.