Vol. 3, No. 4, 2018

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K-theory, local cohomology and tangent spaces to Hilbert schemes

Sen Yang

Vol. 3 (2018), No. 4, 709–722
Abstract

Using K-theory, we construct a map π : TY Hilbp(X) Hyp(ΩXp1) from the tangent space to the Hilbert scheme at a point Y to the local cohomology group. We use this map π to answer (after slight modification) a question by Mark Green and Phillip Griffiths on constructing a map from the tangent space TY Hilbp(X) to the Hilbert scheme at a point Y to the tangent space to the cycle group TZp(X).

Keywords
deformation of cycles, tangent spaces to cycle groups, K-theory, Chern character, tangent spaces to Hilbert schemes, Koszul complex, Newton class, absolute differentials
Mathematical Subject Classification 2010
Primary: 14C25
Milestones
Received: 6 February 2018
Revised: 14 May 2018
Accepted: 30 May 2018
Published: 18 December 2018
Authors
Sen Yang
School of Mathematics and Shing-Tung Yau Center
Southeast University
Nanjing, Jiangsu
China
Yau Mathematical Sciences Center
Tsinghua University
Beijing
China