On explicit birational geometry for weak Fano varieties and polarised Calabi-Yau varieties

Minzhe Zhu

On explicit birational geometry for weak Fano varieties and polarised Calabi-Yau varieties

Algebraic Geometry 2023-01-19 v1

Authors: Minzhe Zhu

Abstract

Given a natural number $l$ and a weak Fano $n$ -fold $X$ with $\operatorname{dim}\overline{\varphi_{-lK_X}(X)}\geq n-1$ , we study the lower bound of the anti-canonical volume and the upper bound of the anti-canonical stability index. The method can also be used to give similar bounds for polarised Calabi-Yau varieties.

Keywords

weak fano varieties polarised calabi-yau varieties birational geometry anti-canonical volume stability index

Cite

@article{arxiv.2301.07462,
  title  = {On explicit birational geometry for weak Fano varieties and polarised Calabi-Yau varieties},
  author = {Minzhe Zhu},
  journal= {arXiv preprint arXiv:2301.07462},
  year   = {2023}
}

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14 pages

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