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Cohen–Macaulay Properties of Thom–Boardman Strata II: The Defining Ideals of Σ i, j
Author(s) -
Fukui Toshizumi,
Weyman Jerzy
Publication year - 2003
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611502013928
Subject(s) - mathematics , normalization (sociology) , gravitational singularity , pure mathematics , mathematics subject classification , closure (psychology) , ring (chemistry) , lens space , mathematical analysis , law , chemistry , organic chemistry , sociology , anthropology , political science
We consider the Zariski closure of Thom–Boardman strata Σ i, j in the jet space for map‐germs (C n , 0) → (C p , 0). We apply the geometric technique of calculating syzygies to the desingularization of Σ i, j constructed by Ronga. We investigate when the normalization of the coordinate ring of Σ i, j is rational in the cases i = n − p + 1 or i = j = 1. We also consider when these coordinate rings are normal with rational singularities. 2000 Mathematics Subject Classification 13D02, 14B05, 14M05, 14M12, 58C25 (primary), 58K20 (secondary).