Permutation-Equivariant Quantum K-Theory X. Quantum Hirzebruch-Riemann-Roch in Genus 0

Abstract

We extract genus 0 consequences of the all genera quantum HRR formula proved in Part IX. This includes re-proving and generalizing the adelic characterization of genus 0 quantum K-theory found in [Givental A., Tonita V., in Symplectic, Poisson, and Noncommutative Geometry, Math. Sci. Res. Inst. Publ., Vol. 62, Cambridge University Press, New York, 2014, 43-91]. Extending some results of Part VIII, we derive the invariance of a certain variety (the ''big J-function''), constructed from the genus 0 descendant potential of permutation-equivariant quantum K-theory, under the action of certain finite difference operators in Novikov's variables, apply this to reconstructing the whole variety from one point on it, and give an explicit description of it in the case of the point target space.