Titlebook: Combinatorial Structures in Algebra and Geometry; NSA 26, Constanța, R Dumitru I. Stamate,Tomasz Szemberg Conference proceedings 2020 Sprin

返老还童

Lecture Notes in Networks and SystemsRecently, chains of increasing symmetric ideals have attracted considerable attention. In this note, we summarize some results and open problems concerning the asymptotic behavior of several algebraic and homological invariants along such chains, including codimension, projective dimension, Castelnuovo-Mumford regularity, and Betti tables.

Contracture

Marc-André Jung,Tim FingscheidtWe present a question which implies a complete positive answer for the Bass-Quillen Conjecture.

担心

Philipp Heidenreich,Abdelhak M. ZoubirOver the last 25 years the study of algebraic, homological and combinatorial properties of powers of ideals has been one of the major topics in Commutative Algebra. In this article, we survey the recent results concerning the associated primes, regularity, depth and Stanley depth of (symbolic) powers of cover ideals of graphs.

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Nearly Normally Torsionfree Ideals,We describe all connected graphs whose edge ideals are nearly normally torsionfree. We also prove that the facet ideal of a special odd cycle is nearly normally torsionfree. Finally, we give a necessary condition for a .-spread principal Borel ideal generated in degree 3 to be nearly normally torsionfree.

CHOIR

Cursory

On the Symbolic Powers of Binomial Edge Ideals,We show that under some conditions, if the initial ideal . of an ideal . in a polynomial ring has the property that its symbolic and ordinary powers coincide, then the ideal . shares the same property. We apply this result to prove the equality between symbolic and ordinary powers for binomial edge ideals with quadratic Gröbner basis.

EXTOL

Multigraded Betti Numbers of Some Path Ideals,We provide formulas for multigraded Betti numbers of path ideals of lines and star graphs.

移植

COKE

Asymptotic Behavior of Symmetric Ideals: A Brief Survey,Recently, chains of increasing symmetric ideals have attracted considerable attention. In this note, we summarize some results and open problems concerning the asymptotic behavior of several algebraic and homological invariants along such chains, including codimension, projective dimension, Castelnuovo-Mumford regularity, and Betti tables.

Latency