Related papers: Linked determinantal loci and limit linear series
In order to prove new existence results in Brill-Noether theory for rank-2 vector bundles with fixed special determinant, we develop foundational definitions and results for limit linear series of higher-rank vector bundles. These include…
We show that limit linear series spaces for chains of curves are reduced. Using new advances in the foundations of limit linear series, we then use degenerations to study the question of connectedness for spaces of linear series with…
Over Cohen--Macaulay rings admitting a pointwise dualizing module, we show that the class of modules of restricted projective dimension bounded by any integer is finitely deconstructible and that the class of modules of restricted flat…
We compute the Euler characteristic of the structure sheaf of the Brill-Noether locus of linear series with special vanishing at up to two marked points. When the Brill-Noether number $\rho$ is zero, we recover the Castelnuovo formula for…
We show that the linked Grassmannian scheme, which arises in a functorial compactification of spaces of limit linear series, and in local models of certain Shimura varieties, is Cohen-Macaulay, reduced, and flat. We give an application to…
Continuing our previous study of modified expected dimensions for rank-2 Brill-Noether loci with prescribed special determinants, we introduce a general framework which applies a priori for arbitrary rank, and use it to prove modified…
We introduce new homological dimensions, namely the Cohen-Macaulay projective, injective and flat dimensions for homologically bounded complexes. Among other things we show that (a) these invariants characterize the Cohen-Macaulay property…
In math.AG/0407496, a new construction of limit linear series is presented which functorializes and compactifies the original construction of Eisenbud and Harris, using a new space called the linked Grassmannian. The boundary of the…
In this paper, we prove a new expected dimension formula for certain rank two Brill-Noether loci with fixed special determinant. This answers a question asked by Osserman and also leads to a new and much simpler proof of a theorem of…
In this paper we address a conjecture by Kleppe and Mir\'o-Roig stating that suitable twists by line bundles (on the smooth locus) of the exterior powers of the normal sheaf of a standard determinantal locus are arithmetically…
In this paper, we prove determinant formulas for the $K$-theory classes of the structure sheaves of degeneracy loci classes associated to vexillary permutations in type $A$. As a consequence we obtain determinant formulas for…
We deduce results on the dimension and connectedness of degeneracy loci of maps of finite modules $f:M\to N$ over a local noetherian ring $(A,{\mathfrak m})$. We show for instance that the expected determinantal bounds on the dimension of…
Let R be a Cohen-Macaulay local ring. It is shown that under some mild conditions, the Cohen-Macaulayness property is preserved under linkage. We also study the connection of (S_n) locus of a horizontally linked module and the attached…
We exhibit how the Hodge-Deligne moduli space of $\lambda$-connections over a smooth projective curve, for stable bundles with fixed determinant, can be understood as the dual of the Atiyah algebroid of the determinant of cohomology line…
Given a generic map between flagged vector bundles on a Cohen-Macaulay variety, we construct maximal Cohen-Macaulay modules with linear resolutions supported on the Schubert-type degeneracy loci. The linear resolution is provided by the…
In the 1990's, Bertram, Feinberg and Mukai examined Brill-Noether loci for vector bundles of rank 2 with fixed canonical determinant, noting that the dimension was always bigger in this case than the naive expectation. We generalize their…
In a previous article (J. Algebra 367 (2012), 142-165) we established axiomatic parametrised Cohen-Macaulay approximation which in particular was applied to pairs consisting of a finite type flat family of Cohen-Macaulay rings and modules.…
In this paper we prove Homological Projective Duality for crepant categorical resolutions of several classes of linear determinantal varieties. By this we mean varieties that are cut out by the minors of a given rank of a n x m matrix of…
We introduce certain quiver analogue of the determinantal variety. We study the Kempf-Lascoux-Weyman's complex associated to a line bundle on the variety. In the case of generalized Kronecker quivers, we give a sufficient condition on when…
In the first part of this paper we study scrollers and linearly joined varieties. A particular class of varieties, of important interest in classical Geometry are Cohen--Macaulay varieties of minimal degree. They appear naturally studying…