@article{1c3cb91bf4cb4c5e88c04762bf4a3f9b,
title = "On vanishing theorems for local systems associated to laurent polynomials",
abstract = "We prove some vanishing theorems for the cohomology groups of local systems associated to Laurent polynomials. In particular, we extend one of the results of Gelfand et al. [Generalized Euler integrals and -hypergeometric functions, Adv. Math. 84 (1990), 255-271] to various directions. In the course of the proof, some properties of vanishing cycles of perverse sheaves and twisted Morse theory are used.",
author = "Alexander Esterov and Kiyoshi Takeuchi",
note = "Funding Information: ESTEROV ALEXANDER TAKEUCHI KIYOSHI National Research University Higher School of Economics , Faculty of Mathematics , 6 Usacheva , 199048 Moscow , Russia email aesterov@hse.ru Institute of Mathematics , University of Tsukuba , 1-1-1, Tennodai , Tsukuba , Ibaraki 305-8571 , Japan email takemicro@nifty.com First author was partially supported by RFBR grant 16-01-00409. 09 2018 18 07 2017 231 1 22 28 10 2014 21 02 2016 07 05 2016 {\textcopyright} 2017 Foundation Nagoya Mathematical Journal 2017 Foundation Nagoya Mathematical Journal We prove some vanishing theorems for the cohomology groups of local systems associated to Laurent polynomials. In particular, we extend one of the results of Gelfand et al. [ Generalized Euler integrals and $A$ - hypergeometric functions , Adv. Math. 84 (1990), 255–271] to various directions. In the course of the proof, some properties of vanishing cycles of perverse sheaves and twisted Morse theory are used. Publisher Copyright: {\textcopyright} 2017 Foundation Nagoya Mathematical Journal .",
year = "2018",
doi = "10.1017/nmj.2017.8",
language = "English",
volume = "231",
pages = "1--22",
journal = "Nagoya Mathematical Journal",
issn = "0027-7630",
publisher = "Nagoya University",
}