Hein, Georg
Curves in IP3 with good restriction of the tangent bundle
Preprint series:
Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976)
- MSC:
- 14F05 Vector bundles, sheaves, related construction, See Also {18F20, 32Lxx, 46M20}
- 14H60 Vector bundles on curves, See also {14F05}
- 14H50 Space curves
- 14D25 Geometric invariants, See also {14L30}
Abstract: Abstract:Restriction of a stable vector bundle on a variety to
a subvariety does not always preserves stability.
Here we consider this situation for the $P^3$ the tangent
bundle $E$ of the projective space and its restriction
to space curves $X$.
We obtain a Shatz-stratification of the Hilbert scheme of
all space curves by generalizing the stratification
defined by S. Shatz of families of vector bundles by their
Harder-Narasimhan polygon to even non reduced schemes.
For space curves of small degree we can characterize the
curves in the strata by properties of the curves and their
embedding.
Furthermore, we show that restriction of the tangent bundle
of the projective space $P^3$ to the general space curve is
stable.