Related papers: A limit linear series moduli scheme
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…
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…
We introduce a notion of limit linear series for nodal curves which are not of compact type. We give a construction of a moduli space of limit linear series, which works also in smoothing families, and we prove a corresponding…
In this note, we describe a theory of linked Hom spaces which complements that of linked Grassmannians. Given two chains of vector bundles linked by maps in both directions, we give conditions for the space of homomorphisms from one chain…
The purpose of this of this paper is to develop the theory of Eisenstein series in the framework of geometric Langlands correspondence. Our construction is based on the study of certain relative compactification of the moduli stack of…
Eisenbud and Harris introduced the theory of limit linear series, and constructed a space parametrizing their limit linear series. Recently, Osserman introduced a new space which compactifies the Eisenbud-Harris construction. In the…
We introduce a formalism of descent of moduli spaces, and use it to produce limit linear series moduli spaces for families of curves in which the components of fibers may have monodromy. We then construct a universal stack of limit linear…
We obtain a sharp bound on the degree of a globally generated vector bundle over a reduced irreducible projective variety defined over an algebraically closed field of characteristic zero. As an application, we obtain a Del Pezzo-Bertini…
The goal of this paper is to unify two lines in a particular area of graph limits. First, we generalize and provide unified treatment of various graph limit concepts by means of a combination of model theory and analysis. Then, as an…
We prove a smoothness result for spaces of linear series with prescribed ramification on twice-marked elliptic curves. In characteristic 0, we then apply the Eisenbud-Harris theory of limit linear series to deduce a new proof of the…
Multigraded linear series generalize the classical morphism to the linear series of a basepoint-free line bundle on a scheme. We investigate the collection of the natural cornering morphisms into elementary bigraded linear series obtained…
We describe the space of Eisenbud-Harris limit linear series on a chain of elliptic curves and compare it with the theory of divisors on tropical chains. Either model allows to compute some invariants of Brill-Noether theory using…
We use the theory of logarithmic line bundles to construct compactifications of spaces of roots of a line bundle on a family of curves, generalising work of a number of authors. This runs via a study of the torsion in the tropical and…
This paper aims at generalizing some geometric properties of Grassmannians of finite dimensional vector spaces to the case of Grassmannnians of infinite dimensional ones, in particular for that of $k((z))$. It is shown that the Determinant…
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…
In the 80's D. Eisenbud and J. Harris developed the general theory of limit linear series, Invent. math. 85 (1986), in order to understand what happens to linear systems and their ramification points on families of non-singular curves…
We introduce a notion of regularity for coherent sheaves on Grassmannians of lines. We use this notion to prove some extension of Evans-Griffith criterion to characterize direct sums of line bundles. We also give a cohomological…
By a grassmannian we understand a usual complex grassmannian or possibly an orthogonal or symplectic grassmannian. We classify, with few exceptions, linear embeddings of grassmannians into larger grassmannians, where the linearity…
A relative Picard theory in the context of graded manifolds is introduced. A Berezinian calculus and a theory of connections over SUSY-curves are systematically developed, and used to prove a Gauss-Bonnet theorem for line bundles in that…
In this paper, we see several basic properties of graded linear series. We firstly see that, if a graded linear series contains an ample series, then so are the pullbacks of the system under birational morphisms. Using this proposition, we…