Unwinding Toric Degenerations and Mirror Symmetry for Grassmannians
Forum of Mathematics, Sigma, Tome 10 (2022)
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The most fundamental example of mirror symmetry compares the Fermat hypersurfaces in $\mathbb {P}^n$ and $\mathbb {P}^n/G$, where G is a finite group that acts on $\mathbb {P}^n$ and preserves the Fermat hypersurface. We generalize this to hypersurfaces in Grassmannians, where the picture is richer and more complex. There is a finite group G that acts on the Grassmannian $\operatorname {{\mathrm {Gr}}}(n,r)$ and preserves an appropriate Calabi–Yau hypersurface. We establish how mirror symmetry, toric degenerations, blow-ups and variation of GIT relate the Calabi–Yau hypersurfaces inside $\operatorname {{\mathrm {Gr}}}(n,r)$ and $\operatorname {{\mathrm {Gr}}}(n,r)/G$. This allows us to describe a compactification of the Eguchi–Hori–Xiong mirror to the Grassmannian, inside a blow-up of the quotient of the Grassmannian by G.
@article{10_1017_fms_2022_98,
author = {Tom Coates and Charles Doran and Elana Kalashnikov},
title = {Unwinding {Toric} {Degenerations} and {Mirror} {Symmetry} for {Grassmannians}},
journal = {Forum of Mathematics, Sigma},
publisher = {mathdoc},
volume = {10},
year = {2022},
doi = {10.1017/fms.2022.98},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2022.98/}
}
TY - JOUR AU - Tom Coates AU - Charles Doran AU - Elana Kalashnikov TI - Unwinding Toric Degenerations and Mirror Symmetry for Grassmannians JO - Forum of Mathematics, Sigma PY - 2022 VL - 10 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.1017/fms.2022.98/ DO - 10.1017/fms.2022.98 LA - en ID - 10_1017_fms_2022_98 ER -
%0 Journal Article %A Tom Coates %A Charles Doran %A Elana Kalashnikov %T Unwinding Toric Degenerations and Mirror Symmetry for Grassmannians %J Forum of Mathematics, Sigma %D 2022 %V 10 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.1017/fms.2022.98/ %R 10.1017/fms.2022.98 %G en %F 10_1017_fms_2022_98
Tom Coates; Charles Doran; Elana Kalashnikov. Unwinding Toric Degenerations and Mirror Symmetry for Grassmannians. Forum of Mathematics, Sigma, Tome 10 (2022). doi: 10.1017/fms.2022.98
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