2025/11/14 by Bisio, Francesco
#13F55 (Primary) 13C40 #13P10 (Secondary) #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2511.11376
For \Bbbk a field, let X a m × n matrix of variables and S=\Bbbk[X]. We consider the determinantal ideal I2 ⊆ S generated by the 2-minors of X. In this paper we find a suitable monomial order over S such that I, the initial ideal of I2 with respect to that order, is level, namely, it is Cohen-Macaulay and the socle of an Artinian reduction of the ℕ-graded algebra S/I is concentrated in only one degree. Moreover, we compare the Betti tables of I2 with the tables of its initial ideals. In the last section, we prove the shellability of the simplicial complex naturally associated to S/I in the case m