By Rick Miranda
During this booklet, Miranda takes the technique that algebraic curves are most sensible encountered for the 1st time over the advanced numbers, the place the reader's classical instinct approximately surfaces, integration, and different techniques should be introduced into play. consequently, many examples of algebraic curves are awarded within the first chapters. during this approach, the booklet starts as a primer on Riemann surfaces, with advanced charts and meromorphic services taking heart degree. however the major examples come from projective curves, and slowly yet definitely the textual content strikes towards the algebraic type. Proofs of the Riemann-Roch and Serre Duality Theorems are provided in an algebraic demeanour, through an version of the adelic facts, expressed thoroughly by way of fixing a Mittag-Leffler challenge. Sheaves and cohomology are brought as a unifying gadget within the latter chapters, in order that their application and naturalness are instantly visible. Requiring a history of a one semester of advanced variable! conception and a 12 months of summary algebra, this can be an outstanding graduate textbook for a second-semester direction in complicated variables or a year-long direction in algebraic geometry.
Read or Download Algebraic Curves and Riemann Surfaces (Graduate Studies in Mathematics, Vol 5) PDF
Similar Algebraic Geometry books
This edited number of chapters, authored via prime specialists, offers a whole and basically self-contained development of 3-fold and 4-fold klt flips. a wide a part of the textual content is a digest of Shokurov's paintings within the box and a concise, whole and pedagogical facts of the lifestyles of 3-fold flips is gifted.
An obtainable textual content introducing algebraic geometries and algebraic teams at complicated undergraduate and early graduate point, this publication develops the language of algebraic geometry from scratch and makes use of it to establish the idea of affine algebraic teams from first ideas. construction at the history fabric from algebraic geometry and algebraic teams, the textual content presents an advent to extra complex and specialized fabric.
Notice: merchandise do have huge Margins. An creation to summary algebraic geometry, with the single must haves being effects from commutative algebra, that are said as wanted, and a few simple topology. greater than four hundred routines allotted during the ebook provide particular examples in addition to extra specialized issues now not taken care of in general textual content, whereas 3 appendices current short money owed of a few parts of present learn.
Additional info for Algebraic Curves and Riemann Surfaces (Graduate Studies in Mathematics, Vol 5)