Arc spaces and the Rogers-Ramanujan identities

DOI10.1007/s11139-012-9401-yzbMath1281.14003arXiv1101.4950OpenAlexW2033673980MaRDI QIDQ1937982

Clemens Bruschek, Jan Schepers, Hussein Mourtada

Publication date: 1 February 2013

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1101.4950

zbMATH Keywords

Gröbner basesRogers-Ramanujan identitiesHilbert-Poincaré seriesarc spaces

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Singularities in algebraic geometry (14B05) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Partition identities; identities of Rogers-Ramanujan type (11P84)

Related Items (17)

Neighborly partitions and the numerators of Rogers–Ramanujan identities ⋮ Deforming spaces of \(m\)-jets of hypersurfaces singularities ⋮ Combinatorial differential algebra of \(x^p\) ⋮ On a Koszul complex related to the principal subspace of the basic vacuum module for \(A_1^{(1)}\) ⋮ Some remarks on associated varieties of vertex operator superalgebras ⋮ Resolutions in local algebra and singularity theory. Abstracts from the workshop held February 5--11, 2023 ⋮ New companions to Gordon identities from commutative algebra ⋮ Nonlinear algebra and applications ⋮ New companions to the Andrews-Gordon identities motivated by commutative algebra ⋮ THE DRINFELD–GRINBERG–KAZHDAN THEOREM IS FALSE FOR SINGULAR ARCS ⋮ Graph schemes, graph series, and modularity ⋮ Looking for a new version of Gordon's identities ⋮ Quadratic ideals and Rogers-Ramanujan recursions ⋮ A framework of Rogers-Ramanujan identities and their arithmetic properties ⋮ Chiral homology of elliptic curves and the Zhu algebra ⋮ Cylindric partitions and some new $A_2$ Rogers–Ramanujan identities ⋮ Even-odd partition identities of Rogers-Ramanujan type

Uses Software

• SINGULAR

Cites Work

• The Nash problem of arcs and the rational double point \(E_{6}\)
• Jet schemes of complex plane branches and equisingularity
• Jet schemes of toric surfaces
• Finite Gröbner bases in infinite dimensional polynomial rings and applications
• Finiteness for the \(k\)-factor model and chirality varieties
• Hilbert functions of graded algebras
• Germs of arcs on singular algebraic varieties and motivic integration
• Arcs and resolution of singularities
• Definable sets, motives and 𝑝-adic integrals
• Motivic generating series for toric surface singularities
• Jet schemes, arc spaces and the Nash problem
• Arcs, cords, and felts — six instances of the linearization principle
• Inversion of adjunction for local complete intersection varieties
• A Motivated Proof of the Rogers-Ramanujan Identities
• Exceptional divisors that are not uniruled belong to the image of the Nash map
• The Jet Scheme of a Monomial Scheme
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