TY - JOUR
T1 - Addition–deletion results for the minimal degree of logarithmic derivations of hyperplane arrangements and maximal Tjurina line arrangements
AU - Abe, Takuro
AU - Dimca, Alexandru
AU - Sticlaru, Gabriel
N1 - Funding Information:
The first author was partially supported by KAKENHI, Fund for the Promotion of Joint International Research (Fostering Joint International Research (A)) 18KK0389. The second author has been supported by the French government, through the Investments in the Future project managed by the National Research Agency (ANR) with the reference number ANR-15-IDEX-01 and by the Romanian Ministry of Research and Innovation, CNCS - UEFISCDI, grant PN-III-P4-ID-PCE-2016-0030, within PNCDI III.
Funding Information:
The first author was partially supported by KAKENHI, Fund for the Promotion of Joint International Research (Fostering Joint International Research (A)) 18KK0389. The second author has been supported by the French government, through the U C A JEDI Investments in the Future project managed by the National Research Agency (ANR) with the reference number ANR-15-IDEX-01 and by the Romanian Ministry of Research and Innovation, CNCS - UEFISCDI, grant PN-III-P4-ID-PCE-2016-0030, within PNCDI III.
Publisher Copyright:
© 2020, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2021/11
Y1 - 2021/11
N2 - We study the change of the minimal degree of a logarithmic derivation of a hyperplane arrangement under the addition or the deletion of a hyperplane and give a number of applications. First, we prove the existence of Tjurina maximal line arrangements in a lot of new situations. Then, starting with Ziegler’s example of a pair of arrangements of d= 9 lines with n3= 6 triple points in addition to some double points, having the same combinatorics, but distinct minimal degree of a logarithmic derivation, we construct new examples of such pairs, for any number d≥ 9 of lines, and any number n3≥ 6 of triple points. Moreover, we show that such examples are not possible for line arrangements having only double and triple points, with n3≤ 5.
AB - We study the change of the minimal degree of a logarithmic derivation of a hyperplane arrangement under the addition or the deletion of a hyperplane and give a number of applications. First, we prove the existence of Tjurina maximal line arrangements in a lot of new situations. Then, starting with Ziegler’s example of a pair of arrangements of d= 9 lines with n3= 6 triple points in addition to some double points, having the same combinatorics, but distinct minimal degree of a logarithmic derivation, we construct new examples of such pairs, for any number d≥ 9 of lines, and any number n3≥ 6 of triple points. Moreover, we show that such examples are not possible for line arrangements having only double and triple points, with n3≤ 5.
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U2 - 10.1007/s10801-020-00986-9
DO - 10.1007/s10801-020-00986-9
M3 - Article
AN - SCOPUS:85096049298
SN - 0925-9899
VL - 54
SP - 739
EP - 766
JO - Journal of Algebraic Combinatorics
JF - Journal of Algebraic Combinatorics
IS - 3
ER -