arXiv subjects

B. Russo

Publications and source records attributed to B. Russo.

3 recordsLinked to original sources

arXiv2000

Families of maximal subbundles of stable vector bundles on curves

Let X be a smooth projective curve of genus g bigger then 2. For any vector bundle E on X let M_k(E) be the scheme of all rank k subbundles of E with maximal degree. For every integers r, k and x with 0 r), we construct a rank r stable vector bundle E such that M_k(E) has an irreducible component of dimension x. Furthermore, if there exists a stable vector bundle F with small Lange's invariant s_k(F) and with M_k(F) `spread enough', then X i s a multiple covering of a curve of genus bigger then 2.

math.AG↗

arXiv1998

Exact sequence of semistable vector bundles on algebraic curves

Let X be a smooth complex projective curve of genus g bigger or equal to 1. If g is bigger than 1 assume further that X is either bielliptic or with general moduli. Under a natural condition on slopes, we prove that there exists a short exact sequence of semistable vector bundles with given ranks and degrees. The importance of the paper consists of the new method adopted for the proves.

math.AG↗

arXiv1997

On a conjecture of Lange

Let C be a projective smooth curve of genus g> 1. Let E be a vector bundle of rank r on C. For each integer r' 0. The conjecture has recently been solved thanks to work of Lange- Narasimhan, Lange-Brambila-Paz, Ballico and the authors. The purpose of this paper is to give a simpler proof of the result valid without further assumptions. The method of proof provides additional information on the geometry of the strata. We can prove that each strata (which is irreducible) is contained in the closure of the following one. We also show the unicity of the maximal subbundle when s\le r'(r-r')(g-1). Our methods can be used to study twisted Brill-Noether loci and to give a new proof of Hirschowitz Theorem about the non-speciality of the tensor product of generic vector bundles.

alg-geom↗