arXiv subjects

A. Hirschowitz

Publications and source records attributed to A. Hirschowitz.

5 recordsLinked to original sources

arXiv2000

An Assympotic Vanishing Theorem for Generic Unions of Multiple Points

In this revised form, the proof of the principal lemma has been simplified and the main theorem has been extended to all characteristics for those varieties which are smooth in codimension one. This principal theorem essentially says the following : given an ample line bundle O(1) on a projective variety X and a fixed upper bound M on the multiplicities, there exists a lower bound D such that any generic union of multiple points of multiplicity at most M imposes independent conditions on the sections of O(d) for d>D. Here a multiple point is the closed subscheme defined by a power m of the ideal of a smooth point in X and m is its multiplicity.

alg-geom↗

arXiv1998

Le probleme de Brill-Noether pour les fibre's de Steiner et application aux courbes gauches

A Steiner bundle over the projective 3-space is the kernel in a trivial bundle of a morphism defined by a matrix of linear forms. We produce various Steiner bundles E of rank n such that E(1) has n-1 sections, the dependency locus of which is a smooth curve.

math.AG↗

arXiv1997

New evidence for Green's conjecture on syzygies of canonical curves

We prove that two weakened forms of Green's conjectures for canonical curves are equivalent when the genus $g$ is odd.

alg-geom↗

arXiv1997

Interpolation on Jets

We show that for any finite generic union of pairs $(x_i,L_i)_i$ where $x_i\in L_i$ is a point of the line $L_i$ in projective $n$-space, the divisors $m_ix_i$ on the $L_i$ have maximal rank with respect to homogeneous $d$ forms for all $d\geq 0$ and all $m_i\geq 0$ modulo the expected numerical restrictions.

alg-geom↗

arXiv1997

Generic Hypersurface Singularities

We give a new differential proof of our result on the maximal rank of generic unions of points of multiplicity two in projective space in degrees greater than five. This simplifies somewhat our proof of the Waring conjecture.

alg-geom↗