An application of wall-crossing to Noether-Lefschetz loci

Soheyla Feyzbakhsh; Richard P. Thomas

An application of wall-crossing to Noether-Lefschetz loci

Algebraic Geometry 2020-07-08 v2

Authors: Soheyla Feyzbakhsh , Richard P. Thomas

Abstract

Consider a smooth projective 3-fold $X$ satisfying the Bogomolov-Gieseker conjecture of Bayer-Macr\`{i}-Toda (such as $\mathbb P^3$ , the quintic threefold or an abelian threefold). Let $L$ be a line bundle supported on a very positive surface in $X$ . If $c_1(L)$ is a primitive cohomology class then we show it has very negative square.

Keywords

wall-crossing noether-lefschetz loci bogomolov-gieseker conjecture line bundle projective 3-fold

Cite

@article{arxiv.1912.01644,
  title  = {An application of wall-crossing to Noether-Lefschetz loci},
  author = {Soheyla Feyzbakhsh and Richard P. Thomas},
  journal= {arXiv preprint arXiv:1912.01644},
  year   = {2020}
}

Comments

Referee's corrections. To appear in Quarterly Journal of Mathematics, special issue dedicated to the memory of Sir Michael Atiyah. 19 pages, appendix by Claire Voisin

An application of wall-crossing to Noether-Lefschetz loci

Abstract

Keywords

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