Generalized elliptic genera and Baker-Akhiezer functions

DOI10.1007/BF01156822zbMath0702.57006MaRDI QIDQ915202

I. M. Krichever

Publication date: 1990

Published in: Mathematical Notes (Search for Journal in Brave)

zbMATH Keywords

generalized elliptic genus of a quasi-complex manifoldunitary \(S^ 1\)- actions on SU-manifolds

Mathematics Subject Classification ID

Compact Lie groups of differentiable transformations (57S15) Characteristic classes and numbers in differential topology (57R20) Index theory and related fixed-point theorems on manifolds (58J20) Elliptic genera (58J26) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15) (mathrm{O})- and (mathrm{SO})-cobordism (57R75) Specialized structures on manifolds (spin manifolds, framed manifolds, etc.) (57R15)

Related Items

Hirzebruch functional equation and elliptic functions of level \(d\) ⋮ Characteristic expansions and multiplicative addition theorems ⋮ Witten genus of generalized complete intersections in products of Grassmannians ⋮ Elliptic genera of level \(N\) on complex \(\pi_{2}\)-finite manifolds ⋮ Rigidity of higher elliptic genera ⋮ Hodge-elliptic genera and how they govern \(K3\) theories ⋮ The Jacobi orientation and the two-variable elliptic genus ⋮ Manifolds of solutions for Hirzebruch functional equations ⋮ Self-dual vertex operator superalgebras and superconformal field theory ⋮ Elliptic genus of singular algebraic varieties and quotients ⋮ Algebraic elliptic cohomology and flops. II: SL-cobordism ⋮ On mod 2 and higher elliptic genera ⋮ Computing the Krichever genus ⋮ Hirzebruch functional equation: classification of solutions ⋮ Cobordisms, manifolds with torus action, and functional equations ⋮ On addition theorems related to elliptic integrals ⋮ Universal formal group for elliptic genus of level \(N\) ⋮ 𝐾-equivalence in birational geometry and characterizations of complex elliptic genera ⋮ On family rigidity theorems. I ⋮ Riemann-Roch theorems and elliptic genus for virtually smooth schemes ⋮ Функциональное уравнение Хирцебруха и эллиптические функции уровня $d$ ⋮ Rigidity and vanishing theorems on ℤ/𝕜 Spin^{𝕔} manifolds ⋮ Algebraic elliptic cohomology theory and flops. I ⋮ Genera defined by hyperelliptic integrals and Siegel modular functions

Cites Work

• Elliptic genera and quantum field theory
• Sur les genres multiplicatifs définis par des intégrales elliptiques. (On multiplicative genera defined by elliptic integrals)
• Elliptic modular functions and elliptic genera
• \(\text{Spin}^c\)-structures and \(S^1\)-actions
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