TY - JOUR
T1 - Alexander duality for the alternative polarizations of strongly stable ideals
AU - Shibata, Kosuke
AU - Yanagawa, Kohji
N1 - Funding Information:
The second author is partially supported by JSPS Grant-in-Aid for Scientific Research (C) 19K03456. We are grateful to Professor Yuji Yoshino for stimulating discussion and valuable comments. We also thank Professor Gunnar Fløystad for telling us about his paper [6].
Publisher Copyright:
© 2020, © 2020 Taylor & Francis Group, LLC.
PY - 2020/7/2
Y1 - 2020/7/2
N2 - We will define the Alexander duality for strongly stable ideals. More precisely, for a strongly stable ideal (Formula presented.) with (Formula presented.) for all (Formula presented.) its dual (Formula presented.) is a strongly stable ideal with (Formula presented.) for all (Formula presented.) This duality has been constructed by Fløystad et al.in a different manner, so we emphasis applications here. For example, we will describe the Hilbert series of the local cohomologies (Formula presented.) using the irreducible decomposition of I (through the Betti numbers of (Formula presented.)).
AB - We will define the Alexander duality for strongly stable ideals. More precisely, for a strongly stable ideal (Formula presented.) with (Formula presented.) for all (Formula presented.) its dual (Formula presented.) is a strongly stable ideal with (Formula presented.) for all (Formula presented.) This duality has been constructed by Fløystad et al.in a different manner, so we emphasis applications here. For example, we will describe the Hilbert series of the local cohomologies (Formula presented.) using the irreducible decomposition of I (through the Betti numbers of (Formula presented.)).
KW - Alexander duality
KW - alternative polarizations
KW - irreducible decomposition (of a monomial ideal)
KW - local cohomology
KW - strongly stable ideals
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U2 - 10.1080/00927872.2020.1726940
DO - 10.1080/00927872.2020.1726940
M3 - Article
AN - SCOPUS:85079805621
SN - 0092-7872
VL - 48
SP - 3011
EP - 3030
JO - Communications in Algebra
JF - Communications in Algebra
IS - 7
ER -