We consider the action of the group PGL4(K) on the smooth cubic surfaces of PK3 (K an algebraically closed field of characteristic zero). We classify, in an explicit way, all the smooth cubic surfaces with nontrivial stabilizer, the corresponding stabilizers and obtain a geometric description of each group in terms of permutations of the Eckardt points, of the 27 lines or of the 45 tritangent planes.
Construction of symmetric cubic surfaces
Brundu, Michela;Logar, Alessandro
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2023-01-01
Abstract
We consider the action of the group PGL4(K) on the smooth cubic surfaces of PK3 (K an algebraically closed field of characteristic zero). We classify, in an explicit way, all the smooth cubic surfaces with nontrivial stabilizer, the corresponding stabilizers and obtain a geometric description of each group in terms of permutations of the Eckardt points, of the 27 lines or of the 45 tritangent planes.File in questo prodotto:
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