Skip to main content
Post Made Community Wiki by Pooya
Source Link
Pooya
  • 91
  • 1
  • 2

For which Calabi-Yau threefolds is SYZ conjecture known to hold?

I would like to know for which Calabi-Yau threefolds SYZ conjecture is known to hold. I am aware of works by Gross-Wilson (Borcea-Voisin CY3s) and Ruan (quintic CY3), but they are quite classical works today and I now wonder if there are any more examples of SYZ. Of course, answer depends on what I mean by "SYZ conjecture", so I am happy with SYZ examples at any level. I also wonder what can one conclude from Gross's many works on this subject.

I am also aware of Auroux's (and his collaborators') work on SYZ for Fano manifolds, but I am mainly interested in CY threefold case. This comment does not exclude any information about their work that might be relevant to CY3 case (I just don't know any relation due to my ignorance).

Thank you for your information.