By Maurizio Cornalba
In recent times there was huge, immense task within the idea of algebraic curves. Many long-standing difficulties were solved utilizing the overall concepts built in algebraic geometry in the course of the 1950's and 1960's. also, unforeseen and deep connections among algebraic curves and differential equations were exposed, and those in flip make clear different classical difficulties in curve idea. it kind of feels reasonable to claim that the speculation of algebraic curves appears to be like totally different now from the way it seemed 15 years in the past; specifically, our present kingdom of data repre sents an important boost past the legacy left by means of the classical geometers corresponding to Noether, Castelnuovo, Enriques, and Severi. those books supply a presentation of 1 of the significant parts of this contemporary job; particularly, the research of linear sequence on either a set curve (Volume I) and on a variable curve (Volume II). Our aim is to provide a accomplished and self-contained account of the extrinsic geometry of algebraic curves, which in our opinion constitutes the most geometric center of the hot advances in curve conception. alongside the way in which we will, after all, talk about appli cations of the speculation of linear sequence to a few classical subject matters (e.g., the geometry of the Riemann theta divisor) in addition to to a few of the present study (e.g., the Kodaira size of the moduli area of curves).
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