Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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SECANT VARIETIES TO THE VARIETY OF REDUCIBLE FORMS

  • Shin, Yong-Su (Department of Mathematics Sungshin Women's University)
  • Received : 2013.09.27
  • Accepted : 2014.01.06
  • Published : 2014.02.15
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Abstract

We completely classify the dimension of secant varieties $Sec_1(\mathbb{X}_{{\lambda},2})$ to the variety of reducible forms in $\mathbf{k}[x_0,x_1,x_2]$ when ${\lambda}=(1,{\cdots},1,3,{\cdots},3$), and also show that they are all non-defective.

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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. https://doi.org/10.4134/JKMS.2012.49.2.405
  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. https://doi.org/10.1016/j.jpaa.2010.04.008
  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. https://doi.org/10.1307/mmj/1220879400
  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. https://doi.org/10.1080/00927872.2012.656783