\(q\)-identities and affinized projective varieties. I: Quadratic monomial ideals

DOI10.1007/S002200050794zbMATH Open0961.14040arXivmath-ph/9902010OpenAlexW1987465937MaRDI QIDQ1976011

Publication date: 27 November 2000

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Abstract: We define the concept of an affinized projective variety and show how one can, in principle, obtain q-identities by different ways of computing the Hilbert series of such a variety. We carry out this program for projective varieties associated to quadratic monomial ideals. The resulting identities have applications in describing systems of quasi-particles containing null-states and can be interpreted as alternating sums of quasi-particle Fock space characters.

Full work available at URL: https://arxiv.org/abs/math-ph/9902010

zbMATH Keywords

Hilbert series \(q\)-identities affinized projective variety Fock space characters quadratic monomial

Mathematics Subject Classification ID

Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) (14N35) Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem) (14R10) Projective techniques in algebraic geometry (14N05)

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