Hirotachi Abo, Ph.D.
College of Science
With UI Since 2006
Department of Mathematics
Ph.D. in Mathematics, Saarland University (Germany), 2002
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 Grassmanns 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 Pm 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.
- National Science Foundation, 2009-2012, "Collaborative Research: Algebraic Geometry of Tensors"