1,720,993 research outputs found
Divisor class group and canonical class of rings defined by ideals of Pfaffians.
No full textIn this paper we study the rings defined by ideals of pfaffians of a skew symmetric matrix of indeterminates. We analyze the case in which the pfaffians are not necessarily of fixed size. We prove that such rings are Cohenl-Macaulay normal domains and we compute the divisor class group and the canonical class. It allows us to determine which of our rings are Gorenstein
Toric rings generated by special stable sets of monomials
No full textIn this paper we consider some subalgebras of the d–th Veronese subring of a polynomial ring, generated by stable subsets of monomials. We prove that these algebras are Koszul, showing that the presentation ideals have Groebner bases of quadrics with respect to suitable term orders. Since the initial monomials of the elements of these Gr ̈obner bases are square–free, it follows by a result of Sturmfels that the algebras under consideration are normal, and thus Cohen–Macaulay
K-algebras generated by Pfaffians
No full textWe study the K-subalgebra of the polynomial ring which is generated by the pfaffians of fixed size. To this end we determine the primary decomposition of products of pfaffian ideals
Invariants of ideals generated by pfaffians
No full textIdeals generated by pfaffians are of interest in commutative algebra and algebraic geometry, as well as in combinatorics. In this article we compute multiplicity and Castelnuovo-Mumford regularity of pfaffian ideals of ladders. We give explicit formulas for some families of ideals, and indicate a procedure that allows to recursively compute the invariants of any pfaffian ideal of ladder. Our approach makes an essential use of liaison theory
Initial algebras of Pfaffian rings
No full textWe compute initial algebras of standard Pfaffian rings via suitable embeddings.
This yields simple proofs that these rings are normal Gorenstein domains, with rational singularities in characteristic and -rational in characteristic . We also determine their -invariants. These methods can also be applied to prove the same properties for rings defined by cogenerated Pfaffian ideals
M-Sequences, Graph Ideals, and Ladder Ideals of Linear Type
No full textIn this paper we study some classes of monomial ideals and ladder determinantal ideals of linear type and their blow-up algebras. Our main tools are Groebner bases and Sagbi bases deformations and the notion of M-sequence of monomials
The h-vector of a Gorenstein codimension three domain
No full textIn this paper we characterize the h-vector of a Gorenstein codimension three domain. Main tool is a lifting theorem which asserts that every codimension three homogeneous Gorenstein ideal with degree matrix verifying certain numerical conditions can be lifted to a codimension three Gorenstein prime ideal
Completely lexsegment ideals.
No full textIn this paper we study ideals which are generated by lexsegments of monomials. In contrast to initial lexsegments, the shadow of an arbitrary lexsegment is in general not again a lexsegment. An ideal generated by a lexsegment is called completely lexsegment, if all iterated shadows of the set of
generators are lexsegments. We characterize all completely lexsegment ideals and describe cases in which they have a linear resolution. We also prove a persistence theorem which states that all iterated shadows of a lexsegment are again lexsegments if the first shadow has this property
On the coordinate ring of pairs of alternating matrices with product zero
No full textGiven an integer n ≥ 2, let X and Y be two generic alternating n × n matrices over a commutative ring k. Denote by k[X, Y ] the polynomial ring with indeterminates the entries of X and Y . Moreover denote by I(XY) the ideal generated by the entries of the product of X and Y . The ring k[X, Y ]/I(XY) is the coordinate ring of the variety of pairs (U, V) of alternating n × n matrices with entries in k, such that UV = 0. In this note we give a k-basis of that coordinate
ring, under the assumption that n! is a unit in k. We use some ideas of De Concini, Procesi and Strickland
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