Sunto
SiaX una varietà quasi-proiettiva su un corpo algebricamente chiuso. SeX è non-singolare è ben noto che si può definire una «teoria dell’intersezione» con valori nell’anello di Chow graduato diX e una teoria delle classi di Chern. In questo lavoro ci occupiamo del problema di come estendere tali risultati al caso in cuiX sia singolare. In particolare si vede come sia possibile definire una «teoria di Chow» suX a partire da una opportuna teoria coomologica (ad es. coomologa singolare, di De Rham, coomologia étale).
Summary
LetX be a quasi-projective variety over an algebraically closed field. WhenX is non singular there is a well known «intersection theory» with values in the graded Chow ring ofX. Here we consider the question of extending this theory to the singular case. In particular: we show how to develop a «Chow theory», starting with a suitable cohomology theory onX (e.g.: Singular cohomology, De Rham cohomology, étale cohomology).
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Pedrini, C. Cicli algebrici sulle varieta’ singolari. Seminario Mat. e. Fis. di Milano 57, 215–245 (1987). https://doi.org/10.1007/BF02925052
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DOI: https://doi.org/10.1007/BF02925052