Contains contributions by over 25 leading international mathematicians in the areas of commutative algebra and algebraic geometry. The text presents developments and results based on, and inspired by, the work of Mario Fiorentini. It covers topics ranging from almost numerical invariants of algebraic curves to deformation of projective schemes.
The projective normality of smooth degree nine varieties; minimal generating sets for a family of monomial curves in A4; on certain spaces associated to tetragonal curves of genus 7 and 8; Gorenstein algebras with pure resolution; smooth specializations of space curves - questions and examples; on codimension two k-Buchsbaum subvarieties of Pn; curves contractable in general surfaces; on Nagata's theorem for the class group II; Catalecticant varieties; bounds for the Betti numbers of shellable simplical complexes and polytopes; generators for the generic rational space curve - low degree cases; equisingularity, multiplicity and dependence; Picard bundles and syzgies of canonical curves; variations on green theorem concerning the Hilbert functions; on the dimension filtration and Cohen-Macaulay filtered modules monomial conjecture and Auslander's delta-invariant; Hilbert function and numerical invariants of closed subschemes of Pn; a deformation of projective schemes. (Part contents).