arXiv subjects

Alexandra Seceleanu

Publications and source records attributed to Alexandra Seceleanu.

57 records · Page 4Linked to original sources

arXiv2011

Syzygy Theorems via Comparison of Order Ideals on a Hypersurface

We introduce a weak order ideal property that suffices for establishing the Evans-Griffith Syzygy Theorem. We study this weak order ideal property in settings that allow for comparison between homological algebra over a local ring $R$ versus a hypersurface ring $R/(x^n)$. Consequently we solve some relevant cases of the Evans-Griffith syzygy conjecture over local rings of unramified mixed characteristic $p$, with the case of syzygies of prime ideals of Cohen-Macaulay local rings of unramified mixed characteristic being noted. We reduce the remaining considerations to modules annihilated by $p^s$, $s>0$, that have finite projective dimension over a hypersurface ring.

math.AC↗

arXiv2011

Ideals with Larger Projective Dimension and Regularity

We define a family of homogeneous ideals with large projective dimension and regularity relative to the number of generators and their common degree. This family subsumes and improves upon constructions given in [Cav04] and [McC]. In particular, we describe a family of three-generated homogeneous ideals in arbitrary characteristic whose projective dimension grows asymptotically as sqrt{d}^(sqrt(d) - 1).

math.AC↗

arXiv2009

The Weak Lefschetz Property and powers of linear forms in K[x,y,z]

We show that an Artinian quotient of K[x, y, z] by an ideal I generated by powers of linear forms has the Weak Lefschetz property. If the syzygy bundle of I is semistable this follows from results of Brenner-Kaid; our proof works without this hypothesis, which typically does not hold.

math.AC↗