Harder–Narasimhan filtration for rank 2 tensors and stable coverings

Proceedings Mathematical Sciences

ALFONSO ZAMORA¹ 

[1] Instituto de Ciencias Matemáticas (CSIC-UAM-UCM-UCM), Nicolás Cabrera -, Campus Cantoblanco UAM, 0 Madrid, Spain$$

关键词: Harder–Narasimhan filtration;    geometric invariant theory;    tensors;    curve coverings;    moduli space;    Kempf;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

We construct a Harder--Narasimhan filtration for rank 2 tensors, where there does not exist any such notion {/it a priori,} as coming from a GIT notion of maximal unstability. The filtration associated to the 1-parameter subgroup of Kempf giving the maximal way to destabilize, in the GIT sense, a point in the parameter space of the construction of the moduli space of rank 2 tensors over a smooth projective complex variety, does not depend on a certain integer used in the construction of the moduli space, for large values of the integer. Hence, this filtration is unique and we define the Harder--Narasimhan filtration for rank 2 tensors as this unique filtration coming from GIT. Symmetric rank 2 tensors over smooth projective complex curves define curve coverings lying on a ruled surface, hence we can translate the stability condition to define stable coverings and characterize the Harder--Narasimhan filtration in terms of intersection theory.

【 授权许可】

Unknown