v The Springer GTM Test - Result

The Springer GTM Test - Result


Algebraic Geometry: A First Course

You are Joe Harris's Algebraic Geometry: A First Course.

You are intended to introduce students to algebraic geometry; to give them a sense of the basic objects considered, the questions asked about them, and the sort of answers one can expect to obtain. You thus emphasize the classical roots of the subject. For readers interested in simply seeing what the subject is about, you avoid the more technical details better treated with the most recent methods. For readers interested in pursuing the subject further, you will provide a basis for understanding the developments of the last half century, which have put the subject on a radically new footing. Based on lectures given at Brown and Harvard Universities, you retain the informal style of the lectures and stress examples throughout; the theory is developed as needed. Your first part is concerned with introducing basic varieties and constructions; you describe, for example, affine and projective varieties, regular and rational maps, and particular classes of varieties such as determinantal varieties and algebraic groups. Your second part discusses attributes of varieties, including dimension, smoothness, tangent spaces and cones, degree, and parameter and moduli spaces.

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The Springer GTM Test
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