21 citations · 62 across the 24 of their papers we have counts for
26 papers · 1 filter
Divisors and harmonic morphisms on metric graphs of pseudocompact type
Benjamin Mascuch, Montserrat Teixidor i Bigas
A metric graph is of pseudocompact type if identifying parallel edges produces a tree. We give a constructive proof that, for such graphs, divisorial -gonality is equivalent to…
Higher order Petri Loci
Montserrat Teixidor I Bigas
Denote by the subset of the moduli space of curves of genus g consisting of those curves that have a linear series of degree d and dimension r for which…
Brill-Noether loci
Montserrat Teixidor i Bigas
Brill-Noether loci are those subsets of the moduli space determined by the existence of a linear series of degree and dimension . By…
Successive extensions of vector bundles on curves
Montserrat Teixidor i Bigas
We show that on a generic curve, a bundle obtained by successive extensions is stable. We compute the dimension of the set of such extensions. We use degeneration methods specializ…
Brill-Noether loci with ramification at two points
Montserrat Teixidor i Bigas
We prove the injectivity of the Petri map for linear series on a general curve with given ramification at two generic points. We also describe the components of such a set of linea…
Coherent systems on the projective line
P. E. Newstead, Montserrat Teixidor i Bigas
It is well known that there are no stable bundles of rank greater than 1 on the projective line. In this paper, our main purpose is to study the existence problem for stable cohere…
Theta divisors and Ulrich bundles on Geometrically ruled surfaces
M. Aprodu, G. Casnati, L. Costa +2
We consider the following question: for which invariants and is there a geometrically ruled surface over a curve of genus with invariant such…
The strong maximal rank conjecture and moduli spaces of curves
Fu Liu, Brian Osserman, Montserrat Teixidor i Bigas +1
Building on recent work of the authors, we use degenerations to chains of elliptic curves to prove two cases of the Aprodu-Farkas strong maximal rank conjecture, in genus and…
Limit linear series and tropical divisors on chains
Alberto López Martín, Montserrat Teixidor i Bigas
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 com…
Limit linear series and ranks of multiplication maps
Fu Liu, Brian Osserman, Montserrat Teixidor I Bigas +1
We develop a new technique for studying ranks of multiplication maps for linear series via limit linear series and degenerations to chains of genus-1 curves. We use this approach t…
Genera of Brill-Noether curves and staircase paths in Young tableaux
Melody Chan, Alberto López Martín, Nathan Pflueger +1
In this paper, we compute the genus of the variety of linear series of rank and degree on a general curve of genus , with ramification at least and at two given…
Linked symplectic forms and limit linear series in rank 2 with special determinant
Brian Osserman, Montserrat Teixidor i Bigas
We generalize the prior linked symplectic Grassmannian construction, applying it to to prove smoothing results for rank-2 limit linear series with fixed special determinant on chai…
Invariants of the Brill-Noether curve
Abel Castorena, Alberto López Martín, Montserrat Teixidor i Bigas
For a projective nonsingular curve of genus , the Brill-Noether locus parametrizes line bundles of degree over with at least sections. When the curve is…
Petri map for vector bundles near good bundles
Abel Castorena, Alberto López Martín, Montserrat Teixidor i Bigas
We show that on a generic curve and under some conditions on the degree and genus, there exists a component B of the locus of stable vector bundles of rank r and degree d with at l…
Linked alternating forms and linked symplectic Grassmannians
Brian Osserman, Montserrat Teixidor i Bigas
Motivated by applications to higher-rank Brill-Noether theory and the Bertram-Feinberg-Mukai conjecture, we introduce the concepts of linked alternating and linked symplectic forms…
Existence of vector bundles of rank two with fixed determinant and sections
Montserrat Teixidor i Bigas
Consider the scheme B_{2,L}^k of stable vector bundles of rank two and fixed determinant L which have at least k sections. Under suitable numerical conditions and for generic L, we…
Injectivity of the Petri map for twisted Brill-Noether loci
Montserrat Teixidor I. Bigas
Let C be a generic curve, E a generic vector bundle on C. Then, for every line bundle on C the twisted Petri map P:H^0(C,L\otimes E)\otimes H^0(C, K\otimes L^*\otimes E^{*})--> H^0…
Brill-Noether Theory for stable vector bundles
Ivona Grzegorczyk, Montserrat Teixidor I. Bigas
This paper gives an overview of the main results of Brill-Noether Theory for vector bundles on algebraic curves.
Petri map for rank two bundles with canonical determinant
Montserrat Teixidor i Bigas
We prove the Bertram-Feinberg-Mukai conjecture for a generic curve of genus and a semistable vector bundle of rank two and determinant on , namely we prove the i…
Singularities of Brill-Noether loci for vector bundles on a curve
Sebastian Casalaina-Martin, Montserrat Teixidor i Bigas
In this paper we consider the singularities of the varieties parameterizing stable vector bundles of fixed rank and degree with sections on a smooth curve of genus at least two. In…
Some examples of vector bundles in the base locus of the generalized theta divisor
Sebastian Casalaina-Martin, Tawanda Gwena, Montserrat Teixidor i Bigas
This paper shows that on the moduli space of semi-stable vector bundles of fixed rank and determinant (of any degree) on a smooth curve of genus at least two, the base locus of the…
Maps between moduli spaces of vector bundles and the base locus of the theta divisor
Tawanda Gwena, Montserrat Teixidor i Bigas
Given a vector bundle of rank and degree on a curve of genus , one can associate to in a natural way several other vector bundles. For example, one can take…
Existence of coherent systems
Montserrat Teixidor i Bigas
A coherent system of type (r,d,k) on a curve C is a pair (E,V) where E is a vector bundle of rank r and degree d and V is a space of sections of E of dimension k. There is a condit…
Syzygies using vector bundles
Montserrat Teixidor i Bigas
This paper studies syzygies of curves that have been embedded in projective space by line bundles of large degree. The proofs take advantage of the relationship between syzygies an…