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

Using K-theory, we construct a map $π : T_{Y} {Hilb}^{p} (X) \to H_{y}^{p} (Ω_{X ∕ ℚ}^{p - 1})$ 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 $T_{Y} {Hilb}^{p} (X)$ to the Hilbert scheme at a point $Y$ to the tangent space to the cycle group $T Z^{p} (X)$ .

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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

Vol. 3, No. 4, 2018

Sen Yang

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification 2010

Milestones

Authors