Algebraic geometers have renewed their curiosity within the interaction among algebraic vector bundles and projective embeddings. New equipment were constructed for questions akin to: what's the geometric content material of syzygies and of bundles derived from them? How can they be used for giving solid compactifications of common households? Which differential strategies are wanted for the examine of households of projective types? those questions are addressed during this cohesive quantity, the place effects, paintings in development, conjectures, and glossy debts of classical rules are offered.
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