Non-symmetric orthogonal geometry of Grothendieck rings of coherent sheaves on projective spaces

1994/09/27 by Gorodentsev, A. L.
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.alg-geom/9409005

Abstract

In this paper we consider orthogonal geometry of the free \protect\ZZ-module K₀(\protect\PP_n) with respect to the non-symmetric unimodular bilinear form χ(E,F)=∑ (-1)^νdim\ext^ν(E,F). We calculate the isometry group of this form and describe invariants of its natural action on K₀(\protect\PP_n). Also we consider some general constructions with non-symmetric unimodular forms. In particular, we discuss orthogonal decomposition of such forms and the action of the braid group on a set of semiorthonormal bases. We formulate a list of natural arithmetical conjectures about semiorthogonal bases of the form χ.

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