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math.AC2026
Symbolic Rees algebras of complementary edge ideals
Antonino Ficarra, Somayeh Moradi, Yuji Muta
Let be a finite simple graph on and let denote its complementary edge ideal in the polynomial ring . We give a combinatorial description, i…
math.AC2026
Serre depth and local cohomology
Antonino Ficarra
We introduce a fundamental homological invariant, called Serre depth, which stratifies Serre's conditions in the same way that depth stratifies the Cohen-Macaulay property. We stud…
math.AC2026
The stable set of associated primes of a complementary edge ideal
Antonino Ficarra
We explicitly determine the associated primes of every power of a complementary edge ideal, prove that they satisfy the persistence property, and compute the -function. I…