On Codimension One Embedding of Simplicial Complexes

Björner and Wachs generalized the definition of shellability by dropping the assumption of purity; they also introduced the $h$-triangle, a doubly-indexed generalization of the $h$-vector which is combinatorially significant for nonpure shellable complexes. Stanley subsequently defined a nonpure simplicial complex to be sequentially Cohen-Macaulay if it satisfies algebraic conditions that generalize the Cohen-Macaulay conditions for pure complexes, so that a nonpure shellable complex is sequentially Cohen-Macaulay. We show that algebraic shifting preserves the $h$-triangle of a simplicial complex $K$ if and only if $K$ is sequentially Cohen-Macaulay. This generalizes a result of Kalai's for the pure case. Immediate consequences include that nonpure shellable complexes and sequentially Cohen-Macaulay complexes have the same set of possible $h$-triangles.

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On submersions of the complex indicatrix

Filomat ◽

10.2298/fil1716081p ◽

2017 ◽

Vol 31 (16) ◽

pp. 5081-5092

Author(s):

Elena Popovicia

Keyword(s):

Fixed Point ◽

Complex Projective Space ◽

Finsler Space ◽

Hermitian Manifold ◽

Almost Hermitian Manifold ◽

Codimension One ◽

Real Submanifold ◽

Fundamental Equations ◽

Complex Projective ◽

Extrinsic Sphere

In this paper we study the complex indicatrix associated to a complex Finsler space as an embedded CR - hypersurface of the holomorphic tangent bundle, considered in a fixed point. Following the study of CR - submanifolds of a K?hler manifold, there are investigated some properties of the complex indicatrix as a real submanifold of codimension one, using the submanifold formulae and the fundamental equations. As a result, the complex indicatrix is an extrinsic sphere of the holomorphic tangent space in each fibre of a complex Finsler bundle. Also, submersions from the complex indicatrix onto an almost Hermitian manifold and some properties that can occur on them are studied. As application, an explicit submersion onto the complex projective space is provided.

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Constructing selections stepwise over cones of simplicial complexes

Topology and its Applications ◽

10.1016/j.topol.2019.107032 ◽

2020 ◽

Vol 275 ◽

pp. 107032

Author(s):

Valentin Gutev

Keyword(s):

Simplicial Complexes

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The Stellar decomposition: A compact representation for simplicial complexes and beyond

Computers & Graphics ◽

10.1016/j.cag.2021.05.002 ◽

2021 ◽

Author(s):

Riccardo Fellegara ◽

Kenneth Weiss ◽

Leila De Floriani

Keyword(s):

Simplicial Complexes ◽

Compact Representation

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Homological percolation transitions in growing simplicial complexes

Chaos An Interdisciplinary Journal of Nonlinear Science ◽

10.1063/5.0047608 ◽

2021 ◽

Vol 31 (4) ◽

pp. 041102

Author(s):

Y. Lee ◽

J. Lee ◽

S. M. Oh ◽

D. Lee ◽

B. Kahng

Keyword(s):

Simplicial Complexes

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Affine cones over cubic surfaces are flexible in codimension one

Forum Mathematicum ◽

10.1515/forum-2020-0191 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

Alexander Perepechko

Keyword(s):

Automorphism Group ◽

Open Subset ◽

Pezzo Surface ◽

Ample Divisor ◽

Transitive Action ◽

Del Pezzo Surface ◽

Codimension One ◽

Cubic Surfaces ◽

Special Automorphism ◽

Del Pezzo

AbstractLet Y be a smooth del Pezzo surface of degree 3 polarized by a very ample divisor that is not proportional to the anticanonical one. Then the affine cone over Y is flexible in codimension one. Equivalently, such a cone has an open subset with an infinitely transitive action of the special automorphism group on it.

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