The paper conjectures that a certain pencil of algebraic cycles on degree-8 Fermat surfaces yields infinitely many distinct special Noether-Lefschetz components, contradicting Harris's finiteness conjecture, and rigorously proves infinite general components for degrees 4 through 9.
On generically non-reduced components of Hilbert schemes of smooth curves
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Special components of Noether-Lefschetz loci
The paper conjectures that a certain pencil of algebraic cycles on degree-8 Fermat surfaces yields infinitely many distinct special Noether-Lefschetz components, contradicting Harris's finiteness conjecture, and rigorously proves infinite general components for degrees 4 through 9.