Publications

Master's and PhD Theses

1. Rank two and rank three vector bundles on the projective fourspace, 2002, PhD thesis, Universität des Saarlandes, Saarbrücken, Germany

2. A projective model of the Shioda modular surface of level 4, 1995, master’s thesis, Tokyo Metropolitan University, Japan

Journal Publications (Refereed)

1. Hirotachi Abo, Irem Portakal, and Luca Sodomaco, A vector bundle approach to Nash equilibria, Advances in Applied Mathematics, 175 (2026) (link to MATHREPO for supplemental material)  

2. Hirotachi Abo, Maria Chiara Brambilla, Francesco Galuppi, and Alessandro Oneto, Non-defectivity of Segre-Veronese varieties, Proceedings of the American Mathematical Society, Series B 11 (2024), 589-602

3. Hirotachi Abo, Robert Lazarsfeld, and Greg Smith, Ramification and discriminants of vector bundles and a quick proof of Bogomorov’s theorem, Rendiconti dell’Istituto di Matematica dell’Università di Trieste, 54 (2022), Art. No. 6

4. Hirotachi Abo, On the discriminant locus of a rank (n-1) vector bundle on Pn-1, Portugaliae Mathematica, 77 (2020), no. 3-4, 299-343 

5. Hirotachi Abo and Nick Vanniewenhoven, Most secant varieties of tangential varieties to Veronese varieties are nondefective, Transactions of the American Mathematical Society 370 (2018), no. 1, 393-420 

6. Hirotachi Abo, David Eklund, Thomas Kahle, and Chris Peterson, Eigenschemes and the Jordan canonical form, Linear Algebra and its Applications 496 (2016), 121-151 

7. Hirotachi Abo: Varieties of completely decomposable forms and their secants, Journal of Algebra 403 (2014), 135-153 

8. Hirotachi Abo and Jia Wan, On Waring’s problem for systems of skew-symmetric forms, Linear Algebra and its Applications 439 (2013), no 8, 2330-2349 

9. Hirotachi Abo and Maria C. Brambilla, On the dimensions of secant varieties of Segre-Veronese varieties, Annali di Matematica Pura ed Applicata (4) 192 (2013), no. 1, 61-92 

10. Hirotachi Abo and Maria C. Brambilla, New examples of defective secant varieties of Segre-Veronese varieties, Collectanea Mathematica. 63 (8) (2012), 287–297

11. Hirotachi Abo, Giorgio Ottaviani, and Chris Peterson, Non-defectivity of Grassmanns of planes, Journal of Algebraic Geometry 21 (2012), 1-20 

12. Hirotachi Abo, On non-defectivity of certain Segre-Veronese varieties, Journal of Symbolic Computation 45 (2010), 1254-1269 

13. Hirotachi Abo and Maria C. Brambilla, Secant varieties of Segre-Veronese varieties Pm x Pn embedded by O(1,2), Experimental Mathematics 18 (2009), 369-384 

14. Hirotachi Abo, Holger Kley, and Chris Peterson, Petersen plane arrangements and a surface with multiple 7-secants, Advances in Geometry 9 (2009), no. 3, 349-369 

15. Hirotachi Abo, Giorgio Ottaviani, and Chris Peterson, Induction for secant varieties of Segre varieties, Transactions of the American Mathematical Society 361 (2009), 767-792 

16. Hirotachi Abo, Stable rank three vector bundles on P4 with Chern classes (c1,c2,c3)=(-2,4,0), Journal of Pure and Applied Algebra 207 (2006), 299-317 

17. Hirotachi Abo and Kristian Ranestad, Construction of rational surfaces of degree 12 in projective fourspace, Journal of Algebraic Geometry 15 (2006), no.2, 323-338 

18. Hirotachi Abo and Kristian Ranestad, Irregular elliptic surfaces in projective fourspace, Mathematische Nachrichten 278 (2005), no.5, 511-524 

19. Hirotachi Abo, Wolfram Decker, and Nobuo Sasakura, An elliptic conic bundle in P4 arising from a stable rank-3 bundle, Mathematische Zeitschrift 229 (1998), 725-741 

20. Hirotachi Abo, Tomohide Terasoma, and Nobuo Sasakura, Quadratic residue graph and Shioda elliptic modular surface S(4), Tokyo Journal of  Mathematics 19 (1996), 263-288

Proceedings 

1. Hirotachi Abo, Anna Seigal, and Bernd Sturmfels, Eigenconfigurations of tensors, Algebraic and Geometric Methods in Discrete Mathematics (San Antonio, TX, 2015), 8-25, Contemporary Mathematics, 685, American Mathematical Society, Providence, RI, 2017 

2. Hirotachi Abo and Chris Peterson, Implementation of Kumar's correspondence, ISSAC 2006, 9-16, ACM, New York 2006

Book Chapter 

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

Others 

1. Hirotachi Abo, Recent developments in the theory of tensor eigenvectors, report for the semester-long thematic program Algebraic Geometry with Applications to TEnsors and Secants (AGATES)

2. Hirotachi Abo, On the discriminant locus of a vector bundle, Proceedings of the Symposium on Algebraic Curves (2017), 1-8 

3. Hirotachi Abo, テンソルの固有ベクトルとその代数幾何学的側面 (Japanese) [Eigenvectors of tensors and their algebro-geometric aspects], the Proceedings of the Symposium on Algebraic Curves (2016), 1-15

4. Hirotachi Abo, Surfer を通して見た曲面 (Japanese) [Looking surfaces through the eyes of Surfer], 数学セミナー [Sugaku Seminar] 588 (2010), 38-43

5. Hirotachi Abo, On three conjectures about the secant defectivity of classically studied varieties, the Proceedings of the Algebraic Geometry Symposium, 2010, 1-8

6. Hirotachi Abo, On the secant defectivity of Segre-Veronese varieties, the Proceedings of the Algebraic Geometry Symposium, 2010, 9-15