0. Introduction. 1.
1. The universal pseudo-quotient for a family of subvarieties. 23.
2. Normal bundles of quadrics in X
The splitting type on lines. 39.
3. Morphisms from quadrics to Grassmannians. 49.
4. Pointwise uniform vector bundles on non-singular quadrics. 57.
5. Theory of extensions of families over Hilbert schemes. 69.
6. Existence of algebraic quotient proof of Theorem 0.3. 93.
A. Appendix. Deformations of vector bundles on infinitesimally
rigid projective varieties with null global z-forms. 97.
References. 105.
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