Sperner property and finite-dimensional Gorenstein algebras associated to matroids

We consider the question of irreducibility of the Hilbert scheme of points ℋilbdℙn and its Gorenstein locus. This locus is known to be reducible for d ≥ 14. For d ≤ 11 the irreducibility of this locus was proved in the series of papers [G. Casnati and R. Notari, On the Gorenstein locus of some punctual Hilbert schemes, J. Pure Appl. Algebra 213(11) (2009) 2055–2074; On the irreducibility and the singularities of Gorenstein locus of the Punctual Hilbert scheme of degree 10, J. Pure Appl. Algebra 215(6) (2011) 1243–1254; Irreducibility of the Gorenstein locus of the Punctual Hilbert Scheme of degree 11, preprint (2012)] and Iarrobino conjectured that the irreducibility holds for d ≤ 13. In this paper, we prove that the subschemes corresponding to the Gorenstein algebras having Hilbert function (1, 5, 5, 1) are smoothable, i.e. lie in the closure of the locus of smooth subschemes. This result completes the proof of irreducibility of the Gorenstein locus of ℋilb12ℙn, see Theorem 2.

Download Full-text

On the Sperner property and Gorenstein Algebras Associated to Matroids

Discrete Mathematics & Theoretical Computer Science ◽

10.46298/dmtcs.3028 ◽

2012 ◽

Vol DMTCS Proceedings vol. AR,... (Proceedings) ◽

Author(s):

Toshiaki Maeno ◽

Yasuhide Numata

Keyword(s):

Vector Space ◽

Boolean Lattice ◽

Sperner Property ◽

Space Lattice ◽

Gorenstein Algebras ◽

Special Cases ◽

International Audience ◽

Lefschetz Property

International audience We introduce a certain class of algebras associated to matroids. We prove the Lefschetz property of the algebras for some special cases. Our result implies the Sperner property for the Boolean lattice and the vector space lattice. Nous présentons une classe d'algèbres associées aux matroïdes. Nous démontrons que dans quelques cas spécifiques, ces algèbres vérifient la propriété de Lefschetz. Notre résultat implique la propriété de Sperner pour l'algèbre de Boole et pour le poset d'espace vectoriel.

Download Full-text

Non-Linear Dynamics of Cardiovascular Variability Signals

Methods of Information in Medicine ◽

10.1055/s-0038-1634981 ◽

1994 ◽

Vol 33 (01) ◽

pp. 81-84 ◽

Cited By ~ 14

Author(s):

S. Cerutti ◽

S. Guzzetti ◽

R. Parola ◽

M.G. Signorini

Keyword(s):

Dimensional Space ◽

Severe Heart Failure ◽

Parametric Models ◽

Deterministic Systems ◽

Finite Dimensional ◽

Return Maps ◽

Pathological Conditions ◽

Non Linear ◽

Space State

Abstract:Long-term regulation of beat-to-beat variability involves several different kinds of controls. A linear approach performed by parametric models enhances the short-term regulation of the autonomic nervous system. Some non-linear long-term regulation can be assessed by the chaotic deterministic approach applied to the beat-to-beat variability of the discrete RR-interval series, extracted from the ECG. For chaotic deterministic systems, trajectories of the state vector describe a strange attractor characterized by a fractal of dimension D. Signals are supposed to be generated by a deterministic and finite dimensional but non-linear dynamic system with trajectories in a multi-dimensional space-state. We estimated the fractal dimension through the Grassberger and Procaccia algorithm and Self-Similarity approaches of the 24-h heart-rate variability (HRV) signal in different physiological and pathological conditions such as severe heart failure, or after heart transplantation. State-space representations through Return Maps are also obtained. Differences between physiological and pathological cases have been assessed and generally a decrease in the system complexity is correlated to pathological conditions.

Download Full-text

Finite-Dimensional Modeling of Network-Induced Delays for Real-Time Control Systems

10.23919/acc.1988.4789881 ◽

1988 ◽

Cited By ~ 1

Author(s):

Asok Ray ◽

Yoram Halevi

Keyword(s):

Control Systems ◽

Real Time ◽

Real Time Control ◽

Time Control ◽

Finite Dimensional ◽

Dimensional Modeling

Download Full-text

A closer look at the stable completion

10.23943/princeton/9780691161686.003.0005 ◽

2017 ◽

Author(s):

Ehud Hrushovski ◽

François Loeser

Keyword(s):

Inverse Limit ◽

Unit Vector ◽

Vector Spaces ◽

Dimensional Vector ◽

Compact Sets ◽

Linear Topology ◽

Topological Embedding ◽

Definable Set ◽

Finite Dimensional ◽

The One

This chapter introduces the concept of stable completion and provides a concrete representation of unit vector Mathematical Double-Struck Capital A superscript n in terms of spaces of semi-lattices, with particular emphasis on the frontier between the definable and the topological categories. It begins by constructing a topological embedding of unit vector Mathematical Double-Struck Capital A superscript n into the inverse limit of a system of spaces of semi-lattices L(Hsubscript d) endowed with the linear topology, where Hsubscript d are finite-dimensional vector spaces. The description is extended to the projective setting. The linear topology is then related to the one induced by the finite level morphism L(Hsubscript d). The chapter also considers the condition that if a definable set in L(Hsubscript d) is an intersection of relatively compact sets, then it is itself relatively compact.

Download Full-text