#### 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 $\pi :{T}_{Y}{Hilb}^{p}\left(X\right)\to {H}_{y}^{p}\left({\Omega }_{X∕ℚ}^{p-1}\right)$ from the tangent space to the Hilbert scheme at a point $Y$ to the local cohomology group. We use this map $\pi$ to answer (after slight modification) a question by Mark Green and Phillip Griffiths on constructing a map from the tangent space ${T}_{Y}{Hilb}^{p}\left(X\right)$ to the Hilbert scheme at a point $Y$ to the tangent space to the cycle group $T\phantom{\rule{0.3em}{0ex}}{Z}^{p}\left(X\right)$.

##### Keywords
deformation of cycles, tangent spaces to cycle groups, K-theory, Chern character, tangent spaces to Hilbert schemes, Koszul complex, Newton class, absolute differentials
Primary: 14C25