TY - JOUR
T1 - Symbolic powers of codimension two Cohen-Macaulay ideals
AU - Cooper, Susan
AU - Fatabbi, Giuliana
AU - Guardo, Elena
AU - Lorenzini, Anna
AU - Migliore, Juan
AU - Nagel, Uwe
AU - Seceleanu, Alexandra
AU - Szpond, Justyna
AU - Tuyl, Adam Van
N1 - Publisher Copyright:
© 2020 Taylor & Francis Group, LLC.
PY - 2020/11/1
Y1 - 2020/11/1
N2 - Let IX be the saturated homogeneous ideal defining a codimension two arithmetically Cohen-Macaulay scheme (Formula presented.) and let (Formula presented.) denote its m-th symbolic power. We are interested in when (Formula presented.) We survey what is known about this problem when X is locally a complete intersection, and in particular, we review the classification of when (Formula presented.) for all (Formula presented.) We then discuss how one might weaken these hypotheses, but still obtain equality between the symbolic and ordinary powers. Finally, we show that this classification allows one to: (1) simplify known results about symbolic powers of ideals of points in (Formula presented.) (2) verify a conjecture of Guardo, Harbourne, and Van Tuyl, and (3) provide additional evidence to a conjecture of Römer.
AB - Let IX be the saturated homogeneous ideal defining a codimension two arithmetically Cohen-Macaulay scheme (Formula presented.) and let (Formula presented.) denote its m-th symbolic power. We are interested in when (Formula presented.) We survey what is known about this problem when X is locally a complete intersection, and in particular, we review the classification of when (Formula presented.) for all (Formula presented.) We then discuss how one might weaken these hypotheses, but still obtain equality between the symbolic and ordinary powers. Finally, we show that this classification allows one to: (1) simplify known results about symbolic powers of ideals of points in (Formula presented.) (2) verify a conjecture of Guardo, Harbourne, and Van Tuyl, and (3) provide additional evidence to a conjecture of Römer.
KW - Symbolic powers
KW - arithmetically Cohen-Macaulay
KW - codimension two
KW - locally complete intersection
KW - points in
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U2 - 10.1080/00927872.2020.1769120
DO - 10.1080/00927872.2020.1769120
M3 - Article
AN - SCOPUS:85087048644
SN - 0092-7872
VL - 48
SP - 4663
EP - 4680
JO - Communications in Algebra
JF - Communications in Algebra
IS - 11
ER -