Algebraic Curves Towards Moduli Spaces /

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...

Full description

Saved in:
Bibliographic Details
Main Author: Kazaryan, Maxim E. (Author)
Format: Electronic eBook
Language:English
Published: Cham : Springer International Publishing, 2018.
Edition:1st ed. 2018.
Series:Moscow Lectures, 2
Subjects:
Algebraic geometry.
Functions of complex variables.
Mathematical physics.
ISBN:9783030029432
ISSN:2522-0314 ;
Online Access: Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Table of Contents:
  • 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.

Similar Items