By Maurizio Cornalba
In recent times there was huge, immense task within the thought of algebraic curves. Many long-standing difficulties were solved utilizing the final ideas constructed in algebraic geometry throughout 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 thought. it sort of feels reasonable to claim that the speculation of algebraic curves appears totally different now from the way it seemed 15 years in the past; specifically, our present country of information repre sents an important develop past the legacy left via the classical geometers comparable to Noether, Castelnuovo, Enriques, and Severi. those books provide a presentation of 1 of the critical parts of this contemporary job; particularly, the examine of linear sequence on either a hard and fast 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 middle of the new advances in curve thought. alongside the best way we will, after all, talk about appli cations of the idea of linear sequence to a few 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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