Tohoku Mathematical Journal
2020
September
SECOND SERIES VOL. 72, NO. 3

Tohoku Math. J.
72 (2020), 451-485

Title ALGEBRAIC CYCLES AND VERRA FOURFOLDS

Author Robert Laterveer

(Received August 20, 2018, revised April 4, 2019)
Abstract. This note is about the Chow ring of Verra fourfolds. For a general Verra fourfold, we show that the Chow group of homologically trivial 1-cycles is generated by conics. We also show that Verra fourfolds admit a multiplicative Chow--Künneth decomposition, and draw some consequences for the intersection product in the Chow ring of Verra fourfolds.

Mathematics Subject Classification. Primary 14C15. Secondary 14C25, 14C30.
Key words and phrases. Algebraic cycles, Chow groups, motives, multiplicative Chow--Künneth decomposition, Beauville's “(weak) splitting property”, Verra fourfolds, hyperkähler varieties.

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