Semistability of logarithmic cotangent bundle on some projective manifolds

Chintapalli, Seshadri ; Iyer, Jaya N. N. (2014) Semistability of logarithmic cotangent bundle on some projective manifolds Communications in Algebra, 42 (4). pp. 1732-1746. ISSN 0092-7872

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Official URL: http://www.tandfonline.com/doi/abs/10.1080/0092787...

Related URL: http://dx.doi.org/10.1080/00927872.2012.748785

Abstract

In this article, we investigate the semistability of logarithmic de Rham sheaves on a smooth projective variety (X, D), under suitable conditions. This is related to existence of Kahler–Einstein metric on the open variety. We investigate this problem when the Picard number is one. Fix a normal crossing divisor D on X and consider the logarithmic de Rham sheaf ΩX (log D) on X. We prove semistability of this sheaf, when the log canonical sheaf KX + D is ample or trivial, or when −KX − D is ample, i.e., when X is a log Fano n-fold of dimension n ≤ 6. We also extend the semistability result for Kawamata coverings, and this gives examples whose Picard number can be greater than one.

Item Type:Article
Source:Copyright of this article belongs to Taylor and Francis Ltd.
Keywords:Logarithmic Fano Manifolds; Logarithmic Cotangent Bundle; Semistability
ID Code:102288
Deposited On:01 Feb 2018 11:03
Last Modified:01 Feb 2018 11:03

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