大野 真裕
| 共通教育部（研究科） | 教授 |
| 共通教育部（学域） | 教授 |
| 情報学専攻 | 教授 |
| Ⅱ類（融合系） | 教授 |
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論文
- Nef vector bundles on a hyperquadric with first Chern class two
Masahiro Ohno
筆頭著者, Forum Mathematicum, Walter de Gruyter GmbH, 出版日 2024年04月24日, 査読付, 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.
研究論文（学術雑誌）, 英語 - 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巻, 掲載ページ 755-781, 出版日 2021年06月19日, 査読付
研究論文（学術雑誌）, 英語 - Nef vector bundles on a quadric surface with the first Chern class (2,1)
Masahiro OHNO
Advances in Geometry, De Gruyter, 20巻, 1号, 掲載ページ 109-116, 出版日 2019年06月21日, 査読付
研究論文（学術雑誌）, 英語 - 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巻, 2号, 掲載ページ 425-458, 出版日 2019年03月27日, 査読付
研究論文（学術雑誌）, 英語 - Nef vector bundles on a projective space with first Chern class 3 and second Chern class 8
Masahiro Ohno
Matematiche, Universita di Catania, 72巻, 2号, 掲載ページ 69-81, 出版日 2017年, 査読付, 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.
研究論文（学術雑誌）, 英語 - 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巻, 2号, 掲載ページ 745-771, 出版日 2016年04月, 査読付, 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.
研究論文（学術雑誌）, 英語 - Maximal minors of a matrix with linear form entries
Hiroya Ito; Atsushi Noma; Masahiro Ohno
LINEAR & MULTILINEAR ALGEBRA, TAYLOR & FRANCIS LTD, 63巻, 8号, 掲載ページ 1599-1606, 出版日 2015年08月, 査読付, 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.
研究論文（学術雑誌）, 英語 - 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巻, 2号, 掲載ページ 397-406, 出版日 2013年, 査読付, 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.
研究論文（学術雑誌）, 英語 - 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巻, 2号, 掲載ページ 315-316, 出版日 2007年, 査読付
研究論文（学術雑誌）, 英語 - Classification of generalized polarized manifolds by their nef values
Masahiro Ohno
ADVANCES IN GEOMETRY, WALTER DE GRUYTER & CO, 6巻, 4号, 掲載ページ 543-599, 出版日 2006年, 査読付, 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.
研究論文（学術雑誌）, 英語 - Adjoint varieties and their secant varieties
H Kaji; M Ohno; O Yasukura
INDAGATIONES MATHEMATICAE-NEW SERIES, ELSEVIER SCIENCE BV, 10巻, 1号, 掲載ページ 45-57, 出版日 1999年03月, 査読付, 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.
研究論文（学術雑誌）, 英語 - On nef values of determinants of ample vector bundles
Masahiro Ohno
数理解析研究所講究録, 京都大学, 1078巻, 掲載ページ 75-85, 出版日 1999年
研究論文（その他学術会議資料等）, 英語 - On degenerate secant varieties whose Gauss maps have the largest images
M Ohno
PACIFIC JOURNAL OF MATHEMATICS, PACIFIC JOURNAL MATHEMATICS, 187巻, 1号, 掲載ページ 151-175, 出版日 1999年01月, 査読付, 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.
研究論文（学術雑誌）, 英語 - On odd dimensional projective manifolds with smallest secant varieties
M Ohno
MATHEMATISCHE ZEITSCHRIFT, SPRINGER VERLAG, 226巻, 3号, 掲載ページ 483-498, 出版日 1997年11月, 査読付
研究論文（学術雑誌）, 英語 - On degenerate secant varieties of secant defect two
M Ohno
MANUSCRIPTA MATHEMATICA, SPRINGER VERLAG, 93巻, 2号, 掲載ページ 189-204, 出版日 1997年06月, 査読付, 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.
研究論文（学術雑誌）, 英語 - AN AFFIRMATIVE ANSWER TO A QUESTION OF CILIBERTO
M OHNO
MANUSCRIPTA MATHEMATICA, SPRINGER VERLAG, 81巻, 3-4号, 掲載ページ 437-443, 出版日 1993年12月, 査読付, 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.
研究論文（学術雑誌）, 英語 - Π^r^P^1^-bundle from which a surjective morphism to Π^m^P^1^ exists
Masahiro Ohno
Geometriae dedicata, KLUWER ACADEMIC PUBL, 44巻, 3号, 掲載ページ 335-347, 出版日 1992年12月, 査読付, 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.
研究論文（学術雑誌）, 英語
