SECANT VARIETIES TO THE VARIETY OF REDUCIBLE FORMS

Title & Authors
SECANT VARIETIES TO THE VARIETY OF REDUCIBLE FORMS
Shin, Yong-Su;

Abstract
We completely classify the dimension of secant varieties $\small{Sec_1(\mathbb{X}_{{\lambda},2})}$ to the variety of reducible forms in $\small{\mathbf{k}[x_0,x_1,x_2]}$ when ${\lambda} Keywords star-configurations;linear star-configurations;secant varieties; Language English Cited by References 1. J. Ahn and Y. S. Shin, The Minimal Free Resolution of A Star-Configuration in$\mathbb{P^n}$and The Weak-Lefschetz Property, J. Korean of Math. Soc. 49 (2012), no. 2, 405-417. 2. J. Ahn and Y. S. Shin, The Minimal Free Resolution of a Fat Star-configuration in$\mathbb{P^n}$, Algebra Colloquium, To appear. 3. E. Arrondo and A. Bernardi, On the variety parameterizing completely decomposable polynomials, J. Pure Appl. Algebra 215 (2011), no. 3, 201-220. 4. J. Alexander and A. Hirschowitz, Polynomial interpolation in several variables, J. Algebraic Geom. 4 (1995), no. 2, 201-222. 5. E. Carlini, L. Chiantini, and A. V. Geramita, Complete intersections on general hypersurfaces, Mich. Math. J. 57 (2008), 121-136. 6. Y. S. Shin, Secants to The Variety of Completely Reducible Forms and The Union of Star-Configurations, Journal of Algebra and its Applications, 11 (2012), no. 6, 1250109 (27 pages). 7. Y. S. Shin, Star-Configurations in$\mathbb{P^2}\$ Having Generic Hilbert Functions and The Weak-Lefschetz Property, Comm. in Algebra 40 (2012), 2226-2242.