By Francesco Russo
introduction to either classical and smooth strategies in projective
algebraic geometry, this monograph treats the geometrical homes of
varieties embedded in projective spaces, their secant and tangent lines,
the habit of tangent linear areas, the algebro-geometric and topological
obstructions to their embedding into smaller projective areas, and the
classification of extremal cases. It
also offers an answer of Hartshorne’s Conjecture on entire Intersections
for the category of quadratic manifolds and new brief proofs of formerly known
results, using the modern instruments of
Mori concept and of rationally hooked up manifolds.
The new method of a few of the
problems thought of should be resumed within the precept that, rather than learning a
special embedded manifold uniruled through strains, one passes to research the original
geometrical estate at the manifold of traces passing via a basic point
and inside the manifold. as soon as this embedded manifold, often of lower
codimension, is classed, one attempts to reconstruct the unique manifold,
following a precept showing additionally in other
areas of geometry akin to projective differential geometry or complex
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On the Geometry of Some Special Projective Varieties (Lecture Notes of the Unione Matematica Italiana) by Francesco Russo