Diptych varieties. II: Polar varieties

Gavin Brown; Miles Reid

Diptych varieties. II: Polar varieties

Algebraic Geometry 2015-07-22 v3

Authors: Gavin Brown , Miles Reid

Abstract

Part I introduced diptych varieties $V_{ABLM}$ and gave a rigorous construction of them in the case $d,e\ge 2$ and $de>4$ . Here we prove the existence of $V_{ABLM}$ in all the cases with $de\le4$ . At the same time we construct some classes of interesting quasihomogeneous spaces for groups such as $\GL(2)\times\G_m^r$ based on the algebra of polars.

Keywords

diptych varieties polar varieties quasihomogeneous spaces algebraic construction group actions

Cite

@article{arxiv.1208.5858,
  title  = {Diptych varieties. II: Polar varieties},
  author = {Gavin Brown and Miles Reid},
  journal= {arXiv preprint arXiv:1208.5858},
  year   = {2015}
}

Comments

24 pages. A tribute to Yujiro Kawamata, to appear in his sixtieth birthday conference proceedings, ASPM 2015. The webpage at http://homepages.warwick.ac.uk/staff/G.Brown/diptych.html contains links to auxiliary material. (First update adds more detail to calculations of polars and includes a new key variety to handle small cases all together. Only minor editing revisions in later update.)

Diptych varieties. II: Polar varieties

Abstract

Keywords

Cite

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