{"title":"A Riemann-Roch formula for singular reductions by circle actions","abstract":[{"text":"We compute a Riemann-Roch formula for the invariant Riemann-Roch number of a\r\nquantizable Hamiltonian $S^1$-manifold $(M,\\omega,\\mathcal{J})$ in terms of the\r\ngeometry of its symplectic quotient, allowing $0$ to be a singular value of the\r\nmoment map $\\mathcal{J}:M\\to\\mathbb{R}$. The formula involves a new explicit\r\nlocal invariant of the singularities. Our approach relies on a complete\r\nsingular stationary phase expansion of the associated Witten integral.","lang":"eng"}],"publication":"arXiv:2302.09894","language":[{"iso":"eng"}],"date_updated":"2024-04-11T12:37:09Z","citation":{"chicago":"Delarue, Benjamin, Louis Ioos, and Pablo Ramacher. “A Riemann-Roch Formula for Singular Reductions by Circle Actions.” <i>ArXiv:2302.09894</i>, 2023.","mla":"Delarue, Benjamin, et al. “A Riemann-Roch Formula for Singular Reductions by Circle Actions.” <i>ArXiv:2302.09894</i>, 2023.","apa":"Delarue, B., Ioos, L., &#38; Ramacher, P. (2023). A Riemann-Roch formula for singular reductions by circle actions. In <i>arXiv:2302.09894</i>.","short":"B. Delarue, L. Ioos, P. Ramacher, ArXiv:2302.09894 (2023).","ieee":"B. Delarue, L. Ioos, and P. Ramacher, “A Riemann-Roch formula for singular reductions by circle actions,” <i>arXiv:2302.09894</i>. 2023.","bibtex":"@article{Delarue_Ioos_Ramacher_2023, title={A Riemann-Roch formula for singular reductions by circle actions}, journal={arXiv:2302.09894}, author={Delarue, Benjamin and Ioos, Louis and Ramacher, Pablo}, year={2023} }","ama":"Delarue B, Ioos L, Ramacher P. A Riemann-Roch formula for singular reductions by circle actions. <i>arXiv:230209894</i>. Published online 2023."},"type":"preprint","department":[{"_id":"548"}],"status":"public","_id":"53411","external_id":{"arxiv":["2302.09894"]},"date_created":"2024-04-11T12:30:42Z","user_id":"70575","author":[{"first_name":"Benjamin","id":"70575","full_name":"Delarue, Benjamin","last_name":"Delarue"},{"first_name":"Louis","last_name":"Ioos","full_name":"Ioos, Louis"},{"first_name":"Pablo","full_name":"Ramacher, Pablo","last_name":"Ramacher"}],"year":"2023"}