Geometric transitions between Calabi-Yau threefolds related to Kustin-Miller unprojections

Abstract

We study Kustin-Miller unprojections between Calabi-Yau threefolds or more precisely the geometric transitions they induce. We use them to connect many families of Calabi-Yau threefolds with Picard number one to the web of Calabi Yau complete intersections. This enables us to find explicit description of a few known families of Calabi-Yau threefolds in terms of equations. Moreover we find two new examples of Calabi-Yau threefolds with Picard group of rank one, described by Pfaffian equations in weighted projective spaces.

arXiv commentto appear in Journal of Geometry and Physics

References in corpus (12)

• Massless Black Holes and Conifolds in String Theory
• Enhanced Gauge Symmetry in Type II String Theory
• Conifold Transitions and Mirror Symmetry for Calabi-Yau Complete Intersections in Grassmannians
• New Higgs Transitions between Dual N=2 String Models
• Geometric Transitions
• Mirror Symmetry and the Moduli Space for Generic Hypersurfaces in Toric Varieties
• Primitive contractions of Calabi-Yau threefolds II
• The Pfaffian Calabi-Yau, its Mirror, and their link to the Grassmannian G(2,7)
• Monodromy calculatons of fourth order equations of Calabi-Yau type
• Quantum cohomology of a Pfaffian Calabi-Yau variety: verifying mirror symmetry predictions
• A cascade of determinantal Calabi--Yau threefolds
• Calabi-Yau construction by smoothing normal crossing varieties

Cited by in corpus (8)

• Parallel Kustin--Miller unprojection with an application to Calabi--Yau geometry
• A counterexample to the birational Torelli problem for Calabi-Yau threefolds
• Intersections of two Grassmannians in ${\mathbf{P}}^9$
• Mirror symmetry for Pfaffian Calabi-Yau 3-folds via conifold transitions
• Classification of double octic Calabi-Yau threefolds
• Mirror Symmetry and Projective Geometry of Fourier-Mukai Partners
• Bilinkage in codimension $3$ and canonical surfaces of degree $18$ in ${\mathbb{P}}^5$
• On the motive of intersections of two Grassmannians in ${\mathbb{P}}^9$