• Refereed Publications
  • Varieties of completely decomposable forms and their secants, preprint. [ pdf].

  • On the dimensions of secant varieties of Segre-Veronese varieties (together with Maria Chiara Brambilla), accepted for publication in Ann. Mat. Pura Appl. [ pdf].

  • New examples of defective secant varieties of Segre-Veronese varieties (together with Maria Chiara Brambilla), accepted for publication in Collect. Math. [ pdf].

  • Non-defectivity of Grassmanns of planes (together with Giorgio Ottaviani and Chris Peterson), J. Algebraic Geom. 21 (2012), 1-20.

  • On non-defectivity of certain Segre-Veronese varieties, J. Symbolic Comput. 45 (2010), 1254-1269.

  • Secant varieties of Segre-Veronese varieties P^m x Pⁿ embedded by the morphism given by O(1,2) (together with Maria Chiara Brambilla), Experiment. Math. 18 (2009), 269-284. [ M2 scripts ].

  • Petersen plane arrangements and a surface with multiple 7-secants (together with Holger P. Kley and Chris Peterson), Adv. Geom. 9 (2009), no. 3, 349-369. [ M2 scripts ].

  • Induction for secant varieties of Segre varieties (together with Giorgio Ottaviani and Chris Peterson), Trans. Amer. Math. Soc. 361 (2009), 767-792.

  • Implementation of Kumar's construction (together with Chris Peterson), ISSAC 2006, 9-16, ACM, New York, 2006.

  • Exterior algebra methods for the construction of rational surfaces in projective fourspace (together with Frank-Olaf Schreyer), Singularities and computer algebra, 1-12, London Math. Soc. Lecture Note Ser., 324, Cambridge Univ. Press, Cambridge, 2006.

  • Stable rank three vector bundles on P⁴ with Chern classes (c₁,c₂,c₃)=(-2,4,0), J. Pure Appl. Algebra 207 (2006), no. 2, 299-317.

  • Construction of rational surfaces of degree 12 in projective fourspace (together with Kristian Ranestad), J. Algebraic Geom. 15 (2006), no. 2, 323-338. [ M2 scripts ]

  • Irregular elliptic surfaces of degree 12 in projective fourspace (together with Kristian Ranestad), Math. Nachr. 278 (2005), no.5, 511-524.

  • An elliptic conic bundle in P⁴ arising from a stable rank-3 vector bundle (together with Wolfram Decker and Noboru Sasakura), Math. Z. 229 (1998), no. 4, 725-741

  • Quadratic residue graph and Shioda elliptic modular surface S(4) (together with Noboru Sasakura and Tomohide Terasoma), Tokyo J. Math. 19 (1996), no. 2, 263-288

• Non-Refereed Publications

  • On the secant defectivity of Segre-Veronese varieties, to appear in Proceeding of the Algebraic Geometry Symposium held at Waseda University, Japan, 2010, [ pdf]

  • On three conjectures about the secant defectivity of classically studied varieties, to appear in Proceeding of the Algebraic Geometry Symposium held at Waseda University, Japan, 2010, [ pdf]

  • Surferを通して見た曲面 (Surfaces we look through the eyes of Surfer), 数学セミナー (Sugaku Seminar) 588 (2010).

• Theses

  • Rank two and rank three vector bundle on the projective fourspace, Ph D Thesis, Saarland University 2002

  • A projective model of the Shioda modular surface of level 4, Master thesis, Tokyo Metropolitan University 1995

Last Updated: January 04 2010 by Hirotachi Abo