Refereed Publications
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Ramification and discriminants of vector bundles
and a quick proof of Bogomolov's theorem (together with Rob
Lazarsfeld and Greg Smith), Rend. Istit. Mat. Univ. Trieste 54
(2022), Art No. 6.
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On the discriminant locus of a rank n-1 vector bundle on
Pn-1 , Port. Math. 77 (2020), no. 3-4, 299-343.
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Most secant varieties of tangential varieties to Veronese
varieties are nondefective (together with Nick
Vannieuwenhoven), Trans. Amer. Math. Soc. 370 (2018) no.1
393-420.
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Eigenconfigurations of tensors (together with Anna Seigal
and Bernd Sturmfels), Algebraic and geometric methods in discrete mathematics, 1-25, Contemp. Math., 685, Amer. Math. Soc., Providence, RI, 2017.
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Eigenschemes and the Jordan canonical form (together with
David Eklund, Thomas Kahle, and Chris Peterson), Linear Algebra
Appl. 496 (2016), 121-151.
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Varieties of completely decomposable forms and their
secants, J. Algebra 403 (2014), 135-153.
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On Waring's problem for systems of skew symmetric forms
(together with Jia Wan), Linear Algebra Appl. 439 (2013), no. 8,
2330-2349.
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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.
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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), 1-20.
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On non-defectivity of certain Segre-Veronese varieties,
J. Symbolic Comput. 45 (2010), 1254-1269.
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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.
[ M2 scripts ].
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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: October 28, 2019 by Hirotachi Abo
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