arXiv subjects

Montserrat Teixidor-i-Bigas

Publications and source records attributed to Montserrat Teixidor-i-Bigas.

3 recordsLinked to original sources

arXiv1997

On Lange's Conjecture

Let C be an algebraic curve of genus g. Let E be a vector bundle of rank n and degree d. Consider among all subbundles F' of E of rank n' those of maximal degree d'. Then s_n'(E)= n'd-nd'\le n'(n-n')g. If E is stable s_n'(E)>0 while if E is generic s_n'(E)\ge n'(n-n')(g-1) . The following statement was conjectured by Lange: If 0<s\le n'(n-n')(g-1), then there exist stable vector bundles with s_n'(E)=s. We prove this result for the generic curve. We also clarify what happens in the interval n'(n-n')(g-1)<s\le n'(n-n')g Our method uses a degeneration argument to a reducible curve. A similar result has been obtained by L.Bambrila-Paz and H.Lange using a different method.

alg-geom↗

arXiv1997

Curves in Grassmannians

This paper considers curves in Grassmannians which are themselves immersed in projective space by the Plucker map. It is shown that for a generic vector bundle of high enough degree, the image curve lies in a proper linear subvariety of this projective space and satisfies good conditions on syzygies as a curve in this subspace. For very small degree and generic vector bundle, the curve is non- degenerate.

alg-geom↗

arXiv1997

Stable extensions by line bundles

Let C be an algebraic curve of genus g. Consider extensions E of a vector bundle F'' of rank n'' by a vector bundle F' of rank n'. The following statement was conjectured by Lange: If 0<n'deg F''-n''degF'\le n'n''(g-1), then there exist extensions like this with E stable. We prove this result for the generic curve when F' is a line bundle. Our method uses a degeneration argument to a reducible curve.

alg-geom↗