By Maurizio Cornalba

Lately there was huge, immense task within the thought of algebraic curves. Many long-standing difficulties were solved utilizing the overall recommendations 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 concept. it kind of feels reasonable to assert that the speculation of algebraic curves seems to be totally different now from the way it seemed 15 years in the past; specifically, our present country of data repre sents an important develop past the legacy left through the classical geometers reminiscent of Noether, Castelnuovo, Enriques, and Severi. those books provide a presentation of 1 of the valuable parts of this contemporary job; particularly, the examine of linear sequence on either a set curve (Volume I) and on a variable curve (Volume II). Our target is to provide a finished 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, in fact, talk about appli cations of the idea of linear sequence to a couple of classical issues (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 house of curves).

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