On the Chow theory of projectivizations

Abstract

In this paper, we prove a decomposition result for the Chow groups of projectivizations of coherent sheaves of homological dimension $\le 1$. In this process, we establish the decomposition of Chow groups for the cases of Cayley's trick and standard flips. Moreover, we apply these results to study the Chow groups of symmetric powers of curves, nested Hilbert schemes of surfaces, and the varieties resolving Voisin maps for cubic fourfolds.

v2. Many grammatical problems fixed. References updated

References in corpus (3)

• Derived categories of (nested) Hilbert schemes
• Motivic decompositions of moduli spaces of vector bundles on curves
• On the Chow theory of Quot schemes of locally free quotients

Cited by in corpus (7)

• Derived categories of flips and cubic hypersurfaces
• Motives and the Pfaffian-Grassmannian equivalence
• On the Chow theory of Quot schemes of locally free quotients
• On the Chow ring of Fano varieties on the Fatighenti-Mongardi list
• On the Chow groups of Plücker hypersurfaces in Grassmannians
• On the motive of codimension 2 linear sections of $Gr(3,6)$
• Some new Fano varieties with a multiplicative Chow-Künneth decomposition