On stability of tangent bundle of toric varieties

被引：0

作者：

Biswas, Indranil ^{[1
]}

Dey, Arijit ^{[2
]}

Genc, Ozhan ^{[3
,4
]}

Poddar, Mainak ^{[5
]}

机构：

[1] Tata Inst Fundamental Res, Sch Math, Mumbai 400005, Maharashtra, India

[2] Indian Inst Technol Madras, Dept Math, Chennai 600036, Tamil Nadu, India

[3] Middle East Tech Univ, Northern Cyprus Campus,Mersin 10, Guzelyurt, Turkey

[4] Jagiellonian Univ, Dept Math & Comp Sci, Ul Prof Stanislawa,Lojasiewicza 6, PL-30348 Krakow, Poland

[5] Indian Inst Sci Educ & Res, Math Dept, Pune 411008, Maharashtra, India

来源：

PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES | 2021年 / 131卷 / 02期

关键词：

Semistable sheaf; tangent bundle; toric variety; Hirzebruch surface; Fano manifold; SHEAVES;

D O I：

10.1007/s12044-021-00623-w

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let X be a nonsingular complex projective toric variety. We address the question of semi-stability as well as stability for the tangent bundle TX. In particular, a complete answer is given when X is a Fano toric variety of dimension four with Picard number at most two, complementing the earlier work of Nakagawa (Tohoku. Math. J.45 (1993) 297-310; 46 (1994) 125-133). We also give an infinite set of examples of Fano toric varieties for which TX is unstable; the dimensions of this collection of varieties are unbounded. Our method is based on the equivariant approach initiated by Klyachko (Izv. Akad. Nauk. SSSR Ser. Mat.53 (1989) 1001-1039, 1135) and developed further by Perling (Math. Nachr. 263/264 (2004) 181-197) and Kool (Moduli spaces of sheaves on toric varieties, Ph.D. thesis (2010) (University of Oxford); Adv. Math. 227 (2011) 1700-1755).

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