Lagrangian subvarieties in the Chow ring of some hyperk\"ahler varieties

Robert Laterveer

Lagrangian subvarieties in the Chow ring of some hyperk\"ahler varieties

Algebraic Geometry 2018-08-30 v1

Authors: Robert Laterveer

Abstract

Let $X$ be a hyperk\"ahler variety, and let $Z\subset X$ be a Lagrangian subvariety. Conjecturally, $Z$ should have trivial intersection with certain parts of the Chow ring of $X$ . We prove this conjecture for certain Hilbert schemes $X$ having a Lagrangian fibration, and $Z\subset X$ a general fibre of the Lagrangian fibration.

Keywords

hyperkähler variety lagrangian subvariety chow ring hilbert scheme lagrangian fibration

Cite

@article{arxiv.1808.09845,
  title  = {Lagrangian subvarieties in the Chow ring of some hyperk\"ahler varieties},
  author = {Robert Laterveer},
  journal= {arXiv preprint arXiv:1808.09845},
  year   = {2018}
}

Comments

28 pages, to appear in Moscow Math. J., comments welcome. arXiv admin note: text overlap with arXiv:1712.05983

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