Equivalence of Mirror Families Constructed from Toric Degenerations of Flag Varieties

Details Equivalence of Mirror Families Constructed from Toric Degenerations of Flag Varieties Equivalence of Mirror Families Constructed from Toric Degenerations of Flag Varieties

2006-10-18

arxiv.org/abs/math/0610563v2

Mathematics

Algebraic Geometry

16 pages

Scientific paper

Batyrev (et. al.) constructed a family of Calabi-Yau varieties using small toric degenerations of the full flag variety G/B. They conjecture this family to be mirror to generic anti-canonical hypersurfaces in G/B. Recently Alexeev and Brion, as a part of their work on toric degenerations of spherical varieties, have constructed many degenerations of G/B. For any such degeneration we construct a family of varieties, which we prove coincides with Batyrev's in the small case. We prove that any two such families are birational, thus proving that mirror families are independent of the choice of degeneration. The birational maps involved are closely related to Berenstein and Zelevinsky's geometric lifting of tropical maps to maps between totally positive varieties.

Affiliated with

Also associated with

No associations

Rating

Equivalence of Mirror Families Constructed from Toric Degenerations of Flag Varieties does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Equivalence of Mirror Families Constructed from Toric Degenerations of Flag Varieties, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Equivalence of Mirror Families Constructed from Toric Degenerations of Flag Varieties will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-99888