On motivic multiplicativity of cyclic covers

Abstract

Let Y be a smooth projective complex variety of dimension n with trivial Chow groups, and let f: X→ Y be a cyclic cover of degree d branched over a smooth ample divisor D∈ |dL|. We show that a naturally constructed Chow--Künneth decomposition of X is m-fold mn-multiplicative for each integer m≥2 and that its stable motivic multiplicativity defect satisfies sd(X)≤ 2dn. If, in addition, each positive-codimension cycle class on Y is supported on D, then a double cover admits motivic $0$-multiplicativity. As a further application, we show that any smooth Gushel--Mukai sixfold admits motivic 0-multiplicativity. Moreover, we establish the sharp modified-diagonal property for all smooth double EPW sextics, confirming a conjecture of O'Grady for these varieties.

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BibTeX RIS

BibTeX

@misc{xu2026motivic,
  title = {{On motivic multiplicativity of cyclic covers}},
  author = {Ze Xu},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.01008},
  eprint = {2611.01008},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.01008},
}

RIS

TY  - UNPB
TI  - On motivic multiplicativity of cyclic covers
AU  - Ze Xu
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.01008
UR  - https://arxiv.org/abs/2611.01008
AB  - Let Y be a smooth projective complex variety of dimension n with trivial Chow groups, and let f: X→ Y be a cyclic cover of degree d branched over a smooth ample divisor D∈ |dL|. We show that a naturally constructed Chow--Künneth decomposition of X is m-fold mn-multiplicative for each integer m≥2 and that its stable motivic multiplicativity defect satisfies sd(X)≤ 2dn. If, in addition, each positive-codimension cycle class on Y is supported on D, then a double cover admits motivic $0$-multiplicativity. As a further application, we show that any smooth Gushel--Mukai sixfold admits motivic 0-multiplicativity. Moreover, we establish the sharp modified-diagonal property for all smooth double EPW sextics, confirming a conjecture of O'Grady for these varieties.
ER  -

Abstract

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