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pro vyhledávání: '"Bigas, Montserrat Teixidor i"'
Autor:
Bigas, Montserrat Teixidor i
Brill-Noether loci ${\mathcal M}^r_{g,d}$ are those subsets of the moduli space ${\mathcal M}_g$ determined by the existence of a linear series of degree $d$ and dimension $r$. By looking at non-singular curves in a neighborhood of a special chain of
Externí odkaz:
http://arxiv.org/abs/2308.10581
Autor:
Bigas, Montserrat Teixidor i
We generalize to vector bundles the techniques introduced for line bundles in prior work of the author with Liu, Osserman and Zhang. We then use this method to prove the injectivity of the Petri map for vector bundles and the surjectivity of a map re
Externí odkaz:
http://arxiv.org/abs/2208.04414
Autor:
Bigas, Montserrat Teixidor i
Publikováno v:
Pacific J. Math. 332 (2024) 385-393
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 specializing the curve to a chain of elliptic components
Externí odkaz:
http://arxiv.org/abs/2207.02124
Autor:
Bigas, Montserrat Teixidor i
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 linear series on a chain of elliptic curves.
Comment: Comments welcome
Comment: Comments welcome
Externí odkaz:
http://arxiv.org/abs/2108.13469
We completely describe the components of expected dimension of the Hilbert Scheme of rational curves of fixed degree $k$ in the moduli space ${\rm SU}_{C}(r,L)$ of semistable vector bundles of rank $r$ and determinant $L$ on a curve $C$. We show that
Externí odkaz:
http://arxiv.org/abs/2007.10511
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 coherent systems on the projective line when the number of sections is large
Externí odkaz:
http://arxiv.org/abs/2001.07114
Publikováno v:
Alg. Number Th. 18 (2024) 1403-1464
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 $22$ and $23$. This constitutes a major step forward in Farkas' program to prov
Externí odkaz:
http://arxiv.org/abs/1808.01290
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 combinatorial metho
Externí odkaz:
http://arxiv.org/abs/1701.06851
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 to prove a purely elementary criterion for proving cases of the Maximal
Externí odkaz:
http://arxiv.org/abs/1701.06592
Publikováno v:
Trans. Amer. Math. Soc. 370 (2018), no. 5, 3405-3439
In this paper, we compute the genus of the variety of linear series of rank $r$ and degree $d$ on a general curve of genus $g$, with ramification at least $\alpha$ and $\beta$ at two given points, when that variety is 1-dimensional. Our proof uses de
Externí odkaz:
http://arxiv.org/abs/1506.00516