Permutation-equivariant quantum K-theory X. Quantum Hirzebruch-Riemann-Roch in genus 0
Abstract
We extract genus consequences of the all genera quantum HRR formula proved in Part IX. This includes re-proving and generalizing the adelic characterization of genus quantum K-theory found in [Givental A., Tonita V., in Symplectic, Poisson, and Noncommutative Geometry, <I>Math. Sci. Res. Inst. Publ.</I>, 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 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.
Keywords
Cite
@article{arxiv.1710.02376,
title = {Permutation-equivariant quantum K-theory X. Quantum Hirzebruch-Riemann-Roch in genus 0},
author = {Alexander Givental},
journal= {arXiv preprint arXiv:1710.02376},
year = {2020}
}
Comments
20 pages, 1 figure; in version 2, the introduction is rewritten to correct the (previously incorrect) construction of variety L_X, and the formulation of the adelic characterization theorem; version 3 (published) improved exposition