MASAHIRO OHNO
| Division of General Education（Graduate School of Informatics and Engineering） | Professor |
| Division of General Education（School of Informatics and Engineering ） | Professor |
| Department of Informatics | Professor |
| Cluster II (Emerging Multi-interdisciplinary Engineering) | Professor |
Researcher Information
Career
- Apr. 2019
電気通信大学大学院情報理工学研究科, 教授 - Apr. 2010 - Mar. 2019
電気通信大学大学院情報理工学研究科, 准教授 - Apr. 2007 - Mar. 2010
電気通信大学電気通信学部, 准教授 - Oct. 1998 - Mar. 2007
The University of Electro-Communications, Assoc. Prof. - Apr. 1998 - Sep. 1998
Japan Society for the Promotion of Science, 特別研究員PD - Apr. 1995 - Mar. 1998
Waseda University, 助手
Educational Background
Research Activity Information
Paper
- Nef vector bundles on a quadric threefold with first Chern class two
Masahiro Ohno
Lead, Proceedings of the Edinburgh Mathematical Society, Cambridge University Press (CUP), 1-40, 22 Jan. 2025, Peer-reviwed, True, Abstract
We classify nef vector bundles on a smooth hyperquadric of dimension three with first Chern class two over an algebraically closed field of characteristic zero. In particular, we see that they are globally generated.
Scientific journal, English - Nef vector bundles on a hyperquadric with first Chern class two
Masahiro Ohno
Lead, Forum Mathematicum, Walter de Gruyter GmbH, 37, 3, 747-763, 24 Apr. 2024, Peer-reviwed, Abstract
We classify nef vector bundles on a smooth hyperquadric of dimension ≥4{\geq 4} with first Chern class twoover an algebraically closed field of characteristic zero.
Scientific journal, English - Nef vector bundles on a projective space or a hyperquadric with the first Chern class small
Masahiro Ohno
Rendiconti del Circolo Matematico di Palermo Series 2, Springer, 71, 755-781, 19 Jun. 2021, Peer-reviwed
Scientific journal, English - Nef vector bundles on a quadric surface with the first Chern class (2,1)
Masahiro OHNO
Advances in Geometry, De Gruyter, 20, 1, 109-116, 21 Jun. 2019, Peer-reviwed
Scientific journal, English - Nef vector bundles on a projective space with first Chern class three
Masahiro Ohno
Rendiconti del Circolo Matematico di Palermo Series 2, Springer-Verlag, 69, 2, 425-458, 27 Mar. 2019, Peer-reviwed
Scientific journal, English - Nef vector bundles on a projective space with first Chern class 3 and second Chern class 8
Masahiro Ohno
Matematiche, Universita di Catania, 72, 2, 69-81, 2017, Peer-reviwed, We describe nef vector bundles on a projective space with first Chern class three and second Chern class eight over an algebraically closed field of characteristic zero by giving them a minimal resolution in terms of a full strong exceptional collection of line bundles.
Scientific journal, English - Spaces of algebraic maps from real projective spaces to toric varieties
Andrzej KonowsKi; Masahiro Ohno; Kohhei Yamaguchi
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, MATH SOC JAPAN, 68, 2, 745-771, Apr. 2016, Peer-reviwed, The problem of approximating the infinite dimensional space of all continuous maps from an algebraic variety X to an algebraic variety Y by finite dimensional spaces of algebraic maps arises in several areas of geometry and mathematical physics. An often considered formulation of the problem (sometimes called the Atiyah-Jones problem after [1]) is to determine a (preferably optimal) integer n(D) such that the inclusion from this finite dimensional algebraic space into the corresponding infinite dimensional one induces isomorphisms of homology (or homotopy) groups through dimension n(D), where D denotes a tuple of integers called the "degree" of the algebraic maps and n(D) -> infinity as D -> infinity. In this paper we investigate this problem in the case when X is a real projective space and Y is a smooth compact toric variety.
Scientific journal, English - Maximal minors of a matrix with linear form entries
Hiroya Ito; Atsushi Noma; Masahiro Ohno
LINEAR & MULTILINEAR ALGEBRA, TAYLOR & FRANCIS LTD, 63, 8, 1599-1606, Aug. 2015, Peer-reviwed, Let P be a matrix whose entries are homogeneous polynomials in n variables of degree one over an algebraically closed field. We show that the maximal minors, say m-minors, of P generate the linear space of homogeneous polynomials of degree m if P has the maximal rank m at every point of the affine n-space except the origin.
Scientific journal, English - A spectral sequence and nef vector bundles of the first Chern class two on hyperquadrics
Masahiro Ohno; Hiroyuki Terakawa
Annali dell'Universita di Ferrara, Springer-Verlag Italia s.r.l., 60, 2, 397-406, 2013, Peer-reviwed, We deduce from Bondal’s theorem a spectral sequence, which yields a description, such as a resolution, of a coherent sheaf in terms of a full strong exceptional sequence. We then apply the sequence to the case of a vector bundle given with some cohomological data on a projective space
we obtain a resolution of the vector bundle in terms of exceptional line bundles, resolution which is different from that obtained by the Beilinson spectral sequence. Finally we list all known nef vector bundles of the first Chern class two on a hyperquadric of dimension greater than three.
Scientific journal, English - Classification of generalized polarized manifolds by their nef values (Addendun vol 6, pg 543, 2006)
Masahiro Ohno
ADVANCES IN GEOMETRY, WALTER DE GRUYTER & CO, 7, 2, 315-316, 2007, Peer-reviwed
Scientific journal, English - Classification of generalized polarized manifolds by their nef values
Masahiro Ohno
ADVANCES IN GEOMETRY, WALTER DE GRUYTER & CO, 6, 4, 543-599, 2006, Peer-reviwed, Let (M,.E) be a generalized polarized manifold, i.e., a pair of an n-dimensional smooth projective variety M and an ample vector bundle E of rank r on M. Let tau be the nef value of a polarized manifold (M, det E), i.e., the minimum of the set of real numbers t such that K-M + t det E is nef; we have tau r <= n + 1 by Mori's theory. In this paper we classify the pairs (M, E) in the following two cases: (1) n - 2 <= tau r and tau >= 1; (2) n + 1 - tau r < tau <= 1.
Scientific journal, English - Adjoint varieties and their secant varieties
H Kaji; M Ohno; O Yasukura
INDAGATIONES MATHEMATICAE-NEW SERIES, ELSEVIER SCIENCE BV, 10, 1, 45-57, Mar. 1999, Peer-reviwed, The purpose of this article is to show how the graded decomposition of complex simple Lie algebras g can be applied to studying adjoint varieties X and their secant varieties Sec X. Firstly quadratic equations defining adjoint varieties are explicitly given. Secondly it is shown that dim Sec X = 2 dim X for adjoint varieties X in two ways: one is based on Terracini's lemma, and the other is on some explicit description of Sec X in terms of an orbit of the adjoint action. Finally it is shown that the contact loci of the secant variety to its embedded tangent space have dimension two if X is adjoint.
Scientific journal, English - On nef values of determinants of ample vector bundles
Masahiro Ohno
数理解析研究所講究録, Kyoto University, 1078, 75-85, 1999
Research society, English - On degenerate secant varieties whose Gauss maps have the largest images
M Ohno
PACIFIC JOURNAL OF MATHEMATICS, PACIFIC JOURNAL MATHEMATICS, 187, 1, 151-175, Jan. 1999, Peer-reviwed, We propose a class of projective manifolds with degenerate secant varieties, which class is wider than that of Scorza varieties, and study some properties of this class of manifolds. For example, we show that there is a strong restriction on dimensions of manifolds in this class. We also give classifications of such manifolds of low dimensions.
Scientific journal, English - On odd dimensional projective manifolds with smallest secant varieties
M Ohno
MATHEMATISCHE ZEITSCHRIFT, SPRINGER VERLAG, 226, 3, 483-498, Nov. 1997, Peer-reviwed
Scientific journal, English - On degenerate secant varieties of secant defect two
M Ohno
MANUSCRIPTA MATHEMATICA, SPRINGER VERLAG, 93, 2, 189-204, Jun. 1997, Peer-reviwed, We study projective manifolds with degenerate secant varieties under assumptions that the secant defect is two and that the Gauss maps of secant varieties have the largest images. In particular we classify 7-dimensional projective manifolds with 13-dimensional degenerate secant varieties whose Gauss maps have 10-dimensional images. We also determine Del Pezzo fibrations over curves with smallest embedded codimension in the case that the degree of a general fiber is three or four.
Scientific journal, English - AN AFFIRMATIVE ANSWER TO A QUESTION OF CILIBERTO
M OHNO
MANUSCRIPTA MATHEMATICA, SPRINGER VERLAG, 81, 3-4, 437-443, Dec. 1993, Peer-reviwed, We give an example of a nondegenerate n-dimensional smooth projective variety X in P-2n+1 with the canonical bundle ample a variety X whose tangent variety TanX has dimension less than 2n over an algebraically closed field of any characteristic when n greater than or equal to 9. This variety X is not ruled by lines and the embedded tangent space at a general point of X intersects X at some other points, so that this yields an affirmative answer to a question of Ciliberto.
Scientific journal, English - PI(R)P1-BUNDLE FROM WHICH A SUBJECTIVE MORPHISM TO PI(M)P1 EXISTS
M OHNO
GEOMETRIAE DEDICATA, KLUWER ACADEMIC PUBL, 44, 3, 335-347, Dec. 1992, Peer-reviwed, Let pi: X --> Y be a morphism of smooth projective varieties over an algebraically closed field k of characteristic not equal to 2 whose closed fibres are all isomorphic to PI(r) P1 and let pi': X --> PI(r) P1 be a surjective morphism. This article gives a sufficient condition concerning pi' and Y under which X is isomorphic to Y x PI(r) P1.
Scientific journal, English
