Pfaffian Calabi-Yau Threefolds and Mirror Symmetry

Nonabelian 2D gauge theories for determinantal Calabi-Yau varieties

“…A nonabelian generalization of this story, possibly along the lines proposed in [45] or in [42,43], could thus shed light on mirror symmetry for non-complete intersection Calabi-Yau varieties. 15 A check on such a proposal could be performed by comparison with mirror constructions in [26] for certain Pfaffian Calabi-Yau threefolds that appear in [7]. We leave this to future work.…”

“…One can study determinantal varieties defined by a linear map between bundles which do not satisfy this property, but the resulting variety may fail to be smooth, even when A is generic. This may be related to the difficulties found by Kanazawa[26] in locating a crepant resolution for certain "Pfaffian-mirror" Calabi-Yau varieties.…”

Open mirror symmetry for pfaffian Calabi-Yau 3-folds

“…Some models which will be treated in later sections are introduced. From now on, we mainly use the notation in [33].…”

“…In this paper, we treat certain non-complete intersection Calabi-Yau manifolds, so-called pfaffian Calabi-Yaus. The (closed) mirror phenomena of this type of Calabi-Yau manifolds were first discussed in [31], and further investigations were done in [32,33]. This type of Calabi-Yau manifolds have very interesting properties in the sense that some of them have two special points in their moduli spaces, around both of which we can consider the mirror phenomena.…”

New mirror pairs of Calabi-Yau orbifolds

“…Mirror pairs of Calabi-Yau manifolds are constructed in the work of Borcea [14], Voisin [42] and Batyrev, Ciocan-Fontanine, Kim and van Straten [8,9]. Conjectural mirror pairs also appear in the work of Rødland [34], Böhm [13] and Kanazawa [30]. Apart from these examples, all known mirror pairs of Calabi-Yau varieties appear as a result of a general construction of Batyrev and Borisov [7] of mirror pairs of complete intersections in Fano toric varieties.…”