Let An(K) be the Kostant form of U(sl + n ) and Γ the monoid generated by the positive roots of sln. For each λ ∈ Λ(n, r) we construct a functor Fλ from the category of finitely generated Γ-graded An(K)-modules to the category of finite-dimensional S(n, r)-modules, with the property that Fλ maps (minimal) projective resolutions of the one-dimensional An(K)module KA to (minimal) projective resol...

Given distinct points p1, . . . , pr of a smooth variety V (over an algebraically closed field k) and positive integers mi, Z = m1p1 + · · · +mrpr denotes the subscheme defined locally at each point pi by I mi i , where Ii is the maximal ideal in the local ring OV,pi at pi of the structure sheaf. More briefly, we say Z is a fat point subscheme of V . In the case that V is P for some n, it is of...

A sparse generic matrix is a matrix whose entries are distinct variables and zeros. Such matrices were studied by Giusti and Merle who computed some invariants of their ideals of maximal minors. In this paper we extend these results by computing a minimal free resolution for all such sparse determinantal ideals. We do so by introducing a technique for pruning minimal free resolutions when a sub...

For a commutative Hopf algebra A over Z/p, where p is a prime integer, we define the Steenrod operations P i in cyclic cohomology of A using a tensor product of a free resolution of the symmetric group S n and the standard resolution of the algebra A over the cyclic category according to Loday (1992). We also compute some of these operations. 1. Introduction. For any prime p, the mod p Steenrod...

Homogeneous bundles on P2 = SL(3)/P can be described by representations of the parabolic subgroup P . In 1966 Ramanan proved that if ρ is an irreducible representation of P then the induced bundle Eρ on P 2 is simple and even stable (see [Ram]). Since P is not a reductive group, there is a lot of indecomposable reducible representations of P and to classify homogeneous bundles on P2 and among t...

This paper studies Ulrich ideals in hypersurface rings. A characterization of is given. Using this characterization, we construct a minimal free resolution an ideal concretely. We also explore ring the form R=k[[X,Y]]/(f).

Let P be a commutative Noetherian ring, ???? an ideal of which is generated by regular sequence length four, f element P, and P¯ the hypersurface ring P?(f). Assume that ????:f grade four Gorenstein P. We give resolution N P¯?????P¯ free P¯-modules. The built from differential graded algebra P?(????:f) P-modules, together with one homotopy map. In particular, we explicit form for matrix factori...

We define an integer graded symplectic Floer cohomology and a Fintushel–Stern type spectral sequence which are new invariants for monotone Lagrangian sub–manifolds and exact isotopes. The Z–graded symplectic Floer cohomology is an integral lifting of the usual ZΣ(L) –graded Floer–Oh cohomology. We prove the Künneth formula for the spectral sequence and an ring structure on it. The ring structur...

If A is a complex hyperplane arrangement, with complement X, we show that the Chen ranks of G = π1(X) are equal to the graded Betti numbers of the linear strand in a minimal, free resolution of the cohomology ring A = H(X, k), viewed as a module over the exterior algebra E on A: θk(G) = dimk Tor E k−1(A, k)k , for k ≥ 2, where k is a field of characteristic 0. The Chen ranks conjecture asserts ...

In recent work, Clark and Tchernev introduced the notion of monomial resolution supported on a poset. In this talk, I will review this notion, and the related notion of monomial resolution supported on a CW complex. I will discuss a result of mine that shows that resolutions supported on a CW complex are also supported on the face poset of a CW complex. This relates to the work of Clark and Tch...