The symplectic-cohomology description of the mirror

About 15 years old · traced to

Let U=Y∖DU=Y\setminus D and let XX be the mirror fiber of the constructed family over s=exp⁡(2πi(B+iω))s=\exp(2\pi i(\mathbf B+i\omega)). Symplectic-cohomology mirror conjecture. There is an isomorphism of C\mathbb C-algebras

SH0(U)≃H0(X,OX),SH^0(U)\simeq H^0(X,\mathcal O_X),

so that the mirror can be constructed as

X=Spec⁡SH0(U).X=\operatorname{Spec}SH^0(U).

The assertion is motivated by the open–closed string map and homological mirror symmetry; the source gives no resolution status.

References

Primary source

Mark Gross, Paul Hacking and Sean Keel, “Mirror symmetry for log Calabi-Yau surfaces I”, arXiv:1106.4977 (2015).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.