The theorem of Mather on generic projections for singular varieties
The theorem of Mather on generic projections of smooth algebraic varieties is also proved for the singular ones.
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arXiv subjects
E. Ballico
Publications and source records attributed to E. Ballico.
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.
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Numerical invariants for bundles on blow-ups
We suggest an effective procedure to calculate numerical invariants for rank two bundles over blown-up surfaces. We study the moduli spaces M_j of bundles on the blown-up plane splitting over the exceptional divisor as O(j)+O(-j). We use the numerical invariants to give a topological decomposition of M_j.
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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.
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Nodal curves and postulation of generic fat points on surfaces
Let X be a smooth projective surface. Here we study the postulation of a general union Z of fat points of X, when most of the connected components of Z have multiplicity 2. This problem is related to the existence of "good" families of curves on X, with prescribed singularities, most of them being nodes, and to the cohomology of suitable line bundles on blowing ups of X. More precise statements are obtained in the case X=P^2.
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