リケラボ論文検索は、全国の大学リポジトリにある学位論文・教授論文を一括検索できる論文検索サービスです。

リケラボ 全国の大学リポジトリにある学位論文・教授論文を一括検索するならリケラボ論文検索大学・研究所にある論文を検索できる

リケラボ 全国の大学リポジトリにある学位論文・教授論文を一括検索するならリケラボ論文検索大学・研究所にある論文を検索できる

大学・研究所にある論文を検索できる 「EXAMPLES OF SINGULAR TORIC VARIETIES WITH CERTAIN NUMERICAL CONDITIONS」の論文概要。リケラボ論文検索は、全国の大学リポジトリにある学位論文・教授論文を一括検索できる論文検索サービスです。

コピーが完了しました

URLをコピーしました

論文の公開元へ論文の公開元へ
書き出し

EXAMPLES OF SINGULAR TORIC VARIETIES WITH CERTAIN NUMERICAL CONDITIONS

Sato, Hiroshi 大阪大学 DOI:10.18910/73737

2020.01

概要

Definition 1.1 [10, Definition 3.1]. Let X be a Q-factorial projective toric d-fold. Put
γ2 = γ2 (X) := D21 + · · · + D2n ∈ N2 (X),
where D1 , . . . , Dn be the torus invariant prime divisors.
If γ2 · S > 0 (resp. ≥ 0) for any subsurface S ⊂ X, then we say that X is γ2 -positive (resp.
γ2 -nef).
When X is smooth, it is expected that γ2 -positive or γ2 -nef toric varieties have good
geometric properties (see [5], [8] and [9]. Also see Questions 1.2 and 1.3 below). We
should remark that 12 γ2 (X) is the second Chern character ch2 (X) of X in this case. It was
confirmed that these properties hold for the case where X is a Q-factorial terminal toric Fano
3-fold in [10]. Therefore, [10] posed the following questions:
Question 1.2 [10, Question 5.4]. ...

この論文で使われている画像

参考文献

[1] D.A. Cox, J.B. Little and H.K. Schenck: Toric varieties, Graduate Studies in Mathematics 124, American

Mathematical Society, Providence, RI, 2011.

[2] O. Fujino and H. Sato: Introduction to the toric Mori theory, Michigan Math. J. 52 (2004), 649–665.

[3] W. Fulton: Introduction to toric varieties, Annals of Mathematics Studies 131, The William H. Roever

Lectures in Geometry, Princeton University Press, Princeton, NJ, 1993.

[4] K. Matsuki: Introduction to the Mori program, Universitext, Springer-Verlag, New York, 2002.

[5] E. Nobili: Classification of Toric 2-Fano 4-folds, Bull. Braz. Math. Soc., New Series 42 (2011), 399–414.

[6] T. Oda: Convex bodies and algebraic geometry, An introduction to the theory of toric varieties, Translated

from the Japanese, Results in Mathematics and Related Areas (3) 15, Springer-Verlag, Berlin, 1988.

[7] M. Reid: Decomposition of toric morphisms; in Arithmetic and geometry, Vol. II, 395–418, Progr. Math.

36, Birkh¨auser Boston, Boston, MA, 1983.

[8] H. Sato: The numerical class of a surface on a toric manifold, Int. J. Math. Math. Sci. 2012, 9 pp.

[9] H. Sato: Toric 2-Fano manifolds and extremal contractions, Proc. Japan Acad. Ser. A Math. Sci. 92 (2016),

121–124.

[10] H. Sato and R. Sumiyoshi: Terminal toric Fano three-folds with certain numerical conditions, to appear in

Kyoto J. Math., arXiv:1806.03784.

Singular Toric Varieties with Numerical Conditions

59

Hiroshi Sato

Department of Applied Mathematics

Faculty of Sciences

Fukuoka University

8–19–1, Nanakuma, Jonan-ku

Fukuoka 814–0180

Japan

e-mail: hirosato@fukuoka-u.ac.jp

Yusuke Suyama

Department of Mathematics

Graduate School of Science

Osaka University

Toyonaka, Osaka 560–0043

Japan

e-mail: y-suyama@cr.math.sci.osaka-u.ac.jp

...

参考文献をもっと見る

全国の大学の
卒論・修論・学位論文

一発検索!

この論文の関連論文を見る