@article{170ee30ef849473ba0c2a5d9dd533452,
title = "Higher Gauss maps of Veronese varieties—A generalization of Boole{\textquoteright}s formula and degree bounds for higher Gauss map images",
abstract = "The image of the higher Gauss map for a projective variety is discussed. The notion of higher Gauss maps here was introduced by Fyodor L. Zak as a generalization of both ordinary Gauss maps and conormal maps. The main result is a closed formula for the degree of those images of Veronese varieties. This yields a generalization of a classical formula by George Boole on the degree of the dual varieties of Veronese varieties in 1844. As an application of our formula, degree bounds for higher Gauss map images of Veronese varieties are given.",
keywords = "Boole{\textquoteright}s formula, Veronese variety, degree bound, dual variety, higher Gauss map",
author = "Hajime Kaji",
note = "Funding Information: The author would like to thank Professor Fyodor L. Zak, who gave me detailed comments and expert advice. The author would like to thank Professor Shigeharu Takayama, too: the present work was started by his question on higher Gauss maps. The author wishes to thank Professor Satoru Fukasawa for useful comments and invaluable advice, and Professor Tomohide Terasoma for useful discussion. Finally the author would like to thank Professor Wu-yen Chuang, Professor Jiun-Cheng Chen, Professor Jungkai Chen and Professor Katsuhisa Furukawa for inviting me to the mini-conference on algebraic geometry (March 6, 2015) at National Center for Theoretical Sciences (NCTS), and for their warm hospitality throughout his stay in Taipei: In fact, the present work was done partly at NCTS. Funding Information: The author is supported by JSPS KAKENHI Grant Number 25400053 and 16K05113. Publisher Copyright: {\textcopyright} 2018, {\textcopyright} 2018 Taylor & Francis.",
year = "2018",
month = sep,
day = "2",
doi = "10.1080/00927872.2018.1435790",
language = "English",
volume = "46",
pages = "4064--4078",
journal = "Communications in Algebra",
issn = "0092-7872",
publisher = "Taylor and Francis Ltd.",
number = "9",
}