Decomposable Cycles and Noether-Lefschetz Loci

We prove that there exist smooth surfaces of degree $d$ in $\PP³$ whose group of rational equivalence classes of decomposable 0-cycles has rank at least $\lfloor \frac{d-1}3\rfloor$.

2010 Mathematics Subject Classification: 14C15

Keywords and Phrases: Decomposable cycles, Noether-Lefschetz loci.

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