Abstract
The tangent space to an algebraic variety at a point can be defined purely algebraically in such a way that it agrees with the concept familiar to students of calculus. The definition generalizes the observation that the tangency of the x-axis to the parabola defined by y = x 2 can be detected by the fact that the polynomial function f (x) = x 2 has a “double root” at x = 0.
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© 2000 Springer Science+Business Media New York
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Smith, K.E., Kahanpää, L., Kekäläinen, P., Traves, W. (2000). Smoothness. In: An Invitation to Algebraic Geometry. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4497-2_6
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DOI: https://doi.org/10.1007/978-1-4757-4497-2_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3195-5
Online ISBN: 978-1-4757-4497-2
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