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Towards an Algebraic Classification of Calabi-Yau Manifolds I: Study of K3 Spaces
We present an inductive algebraic approach to the systematic construction and classification of generalized Calabi-Yau (CY) manifolds in different numbers of complex dimensions, based on Batyrev's
Symmetric Criticality for Tight Knots
We prove a version of symmetric criticality for ropelength-critical knots. Our theorem implies that a knot or link with a symmetric representative has a ropelength-critical configuration with the
On the geometry of sets of positive reach
The reach of a set S in a metric space, denoted reach(S), is the supremal r such that any point within distance r of S has a unique nearest point in S. Sets of positive reach (PR sets) originate in
We apply a universal normal Calabi–Yau algebra to the construction and classification of compact complex n-dimensional spaces with SU(n) holonomy and their fibrations. This algebraic approach
Universal Calabi-Yau algebra: Towards an unification of complex geometry
We present a universal normal algebra suitable for constructing and classifying Calabi–Yau spaces in arbitrary dimensions. This algebraic approach includes natural extensions of reflexive weight
The Classification of the Simply Laced Berger Graphs from Calabi-Yau $CY_3$ spaces
The algebraic approach to the construction of the reflexive polyhedra that yield Calabi-Yau spaces in three or more complex dimensions with K3 fibres reveals graphs that include and generalize the