The paper proves that the tangent degree τ(X) is never 1 when N=2n, establishes linear lower bounds for deg(Tan(X)) when Tan(X) differs from the secant variety, and classifies varieties with τ(X)>1 in small dimensions for N≥2n+1.
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On the tangent degree and the degree of the tangent variety of a projective variety
The paper proves that the tangent degree τ(X) is never 1 when N=2n, establishes linear lower bounds for deg(Tan(X)) when Tan(X) differs from the secant variety, and classifies varieties with τ(X)>1 in small dimensions for N≥2n+1.