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We define model structures on exact categories, which we call exact model structures. We look at the relationship between these model structures and cotorsion pairs on the exact category. In particular, when the underlying category is weakly idempotent complete, we get Hovey’s one-to-one...
We study the effects of subgroup distortion in the wreath products A wr Z , where A is finitely generated abelian. We show that every finitely generated subgroup of A wr Z has distortion function equivalent to some polynomial. Moreover, for A infinite, and for any polynomial l k , there is a 2...
We give algorithms for computing multiplier ideals using Gröbner bases in Weyl algebras. To this end, we define a modification of Budur–Mustaţaˇ–Saito’s generalized Bernstein–Sato polynomial. We present several examples computed by our algorithm.
Expansions of abelian categories are introduced. These are certain functors between abelian categories and provide a tool for induction/reduction arguments. Expansions arise naturally in the study of coherent sheaves on weighted projective lines; this is illustrated by various applications.
Let X ( 1 , d ) ( n , m ) denote the Segre–Veronese embedding of P n × P m via the sections of the sheaf O ( 1 , d ) . We study the dimensions of higher secant varieties of X ( 1 , d ) ( n , m ) and we prove that there is no defective s th secant variety, except possibly for n values of s ....
Complete hypersurfaces of dimension at least 2 and multiplicity at least 4 have wild Cohen–Macaulay type.
We examine the dual of the so-called “hit problem”, the latter being the problem of determining a minimal generating set for the cohomology of products of infinite projective spaces as a module over the Steenrod Algebra A at the prime 2. The dual problem is to determine the set of A...
Let F be a field of characteristic p . We show that Hom F Σ n ( S λ , S μ ) can have arbitrarily large dimension as n and p grow, where S λ and S μ are Specht modules for the symmetric group Σ n . Similar results hold for the Weyl modules of the general linear group. Every previously...
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