Derived equivalences of K3 surfaces and twined elliptic genera

DOI10.1186/s40687-015-0050-9zbMath1403.11040arXiv1506.06198OpenAlexW2963538771WikidataQ59479361 ScholiaQ59479361MaRDI QIDQ268406

Sander Mack-Crane, John F. R. Duncan

Publication date: 15 April 2016

Published in: Research in the Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.06198

zbMATH Keywords

moonshine moduleLeech latticecomplex K3 surfaces

Mathematics Subject Classification ID

Vertex operators; vertex operator algebras and related structures (17B69) (K3) surfaces and Enriques surfaces (14J28) Elliptic genera (58J26) Jacobi forms (11F50) Representations of sporadic groups (20C34) Applications of group representations to physics and other areas of science (20C35)

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Cites Work

• Umbral moonshine and the Niemeier lattices
• Proof of the umbral moonshine conjecture
• Moonshine
• Mock modular Mathieu moonshine modules
• Much ado about Mathieu
• On the elliptic genera of manifolds of Spin(7) holonomy
• Modular invariance for twisted modules over a vertex operator superalgebra
• Rademacher sums, moonshine and gravity
• Umbral moonshine
• Elliptic genera and quantum field theory
• Modular invariance of vertex operator algebras satisfying \(C_2\)-cofiniteness
• \(K3\) surfaces, \({\mathcal N}=4\) dyons and the Mathieu group \(M_{24}\)
• Derived equivalences of K3 surfaces and orientation
• Fifteen characterizations of rational double points and simple critical points
• The theory of Jacobi forms
• Modularity in orbifold theory for vertex operator superalgebras
• Fourier-Mukai and Nahm transforms in geometry and mathematical physics
• Super-moonshine for Conway's largest sporadic group
• The automorphism group of Leech lattice and elliptic modular functions
• Infinite-dimensional Lie algebras, theta functions and modular forms
• On the classification of integral even unimodular 24-dimensional quadratic forms
• Two constructions of affine Lie algebra representations and boson-fermion correspondence in quantum field theory
• A hyperbolic Kac-Moody algebra and the theory of Siegel modular forms of genus 2
• Elliptic curves and modular forms in algebraic topology. Proceedings of a conference held at the Institute for Advanced Study, Princeton, NJ, Sept. 15-17, 1986
• The genus-zero problem for \(n| h\)-type groups
• Nonabelian orbifolds and the boson-fermion correspondence
• Introduction to vertex operator algebras and their representations
• On two geometric theta lifts
• Super vertex algebras, meromorphic Jacobi forms and umbral moonshine
• Monstrous moonshine and monstrous Lie superalgebras
• Twisted modules over vertex algebras on algebraic curves
• A modular invariance on the theta functions defined on vertex operator algebras
• Mathieu twining characters for \(K3\)
• Mathieu moonshine in the elliptic genus of K3
• Meromorphic Jacobi forms of half-integral index and umbral moonshine modules
• Maass-Jacobi Poincaré series and Mathieu moonshine
• Umbral moonshine and \(K3\) surfaces
• Symmetries of \(K3\) sigma models
• On Rademacher sums, the largest Mathieu group and the holographic modularity of moonshine
• The umbral moonshine module for the unique unimodular Niemeier root system
• Elliptic genus and vertex operator algebras
• Stability conditions on \(K3\) surfaces
• The \(f(q)\) mock theta function conjecture and partition ranks
• On the simple group of D.G. Higman and C.C. Sims
• A simple group of order 44,352,000
• A characterisation of Leech's lattice
• Definite quadratische Formen der Dimension 24 und Diskriminante 1
• Introduction to stability conditions
• VERTEX OPERATOR ALGEBRAS AND WEAK JACOBI FORMS
• THE MOONSHINE MODULE FOR CONWAY’S GROUP
• Elliptic Modular Forms and Their Applications
• A natural representation of the Fischer-Griess Monster with the modular function J as character
• Modular Functions Arising from Some Finite Groups
• Vertex algebras, Kac-Moody algebras, and the Monster
• Monstrous Moonshine
• Finite Groups and Modular Functions
• Some Numerology between the Fischer-Griess Monster and the Elliptic Modular Function
• Lorentzian forms for the Leech lattice
• Spinor Construction of Vertex Operator Algebras, Triality, and 𝐸⁽¹⁾₈
• More on replicable functions
• SIMPLE GRADED RINGS OF SIEGEL MODULAR FORMS, DIFFERENTIAL OPERATORS AND BORCHERDS PRODUCTS
• Congruence Subgroups of PSL(2, Z) of Genus Less than or Equal to 24
• Modular invariance of characters of vertex operator algebras
• Notes on the K3 Surface and the Mathieu GroupM₂₄
• Classical and Umbral Moonshine: Connections and $p$-adic Properties
• Vertex operator superalgebras and odd trace functions
• On derived categories of K3 surfaces, symplectic automorphisms and the Conway group
• Weight one Jacobi forms and umbral moonshine
• Some Sphere Packings in Higher Space
• Notes on Sphere Packings
• A Group of Order 8,315,553,613,086,720,000
• A PERFECT GROUP OF ORDER 8,315,553,613,086,720,000 AND THE SPORADIC SIMPLE GROUPS
• A hiker's guide to \(K3\). Aspects of \(N=(4,4)\) superconformal field theory with central charge \(c=6\)
• Modular-invariance of trace functions in orbifold theory and generalized Moonshine.
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