Hirotachi Abo

My research interests lie on objects in algebraic geometry, commutative algebra, and multi-linear algebra. My current research focus is on the study of problems in multi-linear algebra from an algebro-geometric viewpoint.

• On Waring's problem for systems of skew-symmetric forms, (together with Jia Wan) Linear Algebra Appl. 439 (2013), no. 8, 2330–2349.
• Varieties of completely decomposable forms and their secants. J. Algebra 403 (2014), 135–153.
• On the dimensions of secant varieties of Segre-Veronese varieties (together with Maria Chiara Brambilla), Ann. Mat. Pura Appl.(4) 192 (2013), no. 1, 61-92.
• New examples of defective secant varieties of Segre-Veronese varieties (together with Maria Chiara Brambilla), Collect. Math. 63 (2012), no. 3, 287-297.
• Non-defectivity of Grassmannians of planes (together with Giorgio Ottaviani and Chris Peterson), J. Algebraic Geom. 21 (2012)m no. 1, 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.
• 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.
• Induction for secant varieties of Segre varieties (together with Giorgio Ottaviani and Chris Peterson), Trans. Amer. Math. Soc. 361 (2009), 767-792.

Research Grant

• National Science Foundation, 2009-2012, "Collaborative Research: Algebraic Geometry of Tensors"