Deformation of K-theoretic cycles

2016/03/03 by Yang, Sen
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1603.01008

Abstract

By using higher K-theory, we study deformation theory of K-theoretic cycles. As an application, we answer two questions posed by Mark Green and Philip Griffiths: (1). How to define tangent spaces to cycle class groups in general? (2). Obstruction issues. The highlight is the appearance of negative K-groups which detects the obstructions to deforming cycles.

Related

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• Eliminate obstructions: curves on a 3-fold
• Deformations and automorphisms: a framework for globalizing local tangent and obstruction spaces
• Higher algebraic K-theory and tangent spaces to Chow groups
• Deformation theory from the point of view of fibered categories