Complete intersection Calabi--Yau manifolds with respect to homogeneous vector bundles on Grassmannians

Abstract

Based on the method by [Küc95], we give a procedure to list up all complete intersection Calabi--Yau manifolds with respect to direct sums of irreducible homogeneous vector bundles on Grassmannians for each dimension. In particular, we give a classification of such Calabi--Yau 3-folds and determine their topological invariants. We also give alternative descriptions for some of them.

25 pages, to appear in Math. Z

References in corpus (2)

• The class of the affine line is a zero divisor in the Grothendieck ring: via $G_2$-Grassmannians
• Mirror symmetry for Pfaffian Calabi-Yau 3-folds via conifold transitions

Cited by in corpus (3)

• Bounds for smooth Fano weighted complete intersections
• The class of the affine line is a zero divisor in the Grothendieck ring: via $G_2$-Grassmannians
• Categorical generic fiber