Federico Mangano - Academia.edu (original) (raw)
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Papers by Federico Mangano
This thesis will focus on the study of the relationship that exists between Del Pezzo surfaces, a... more This thesis will focus on the study of the relationship that exists between Del Pezzo surfaces, a kind of surface defined as "a smooth birationally trivial surface V on which the anticanonical sheaf is ample" and counting points in the projective plane P2(k) built over a finite field k. The result allowing us to to link the two concepts says that a Del Pezzo surface of degree d bigger that 1 is isomorphic to the blowup up of 9-d points in P2(k). Once we have settled the relationship between the two concepts the results will revolve around counting n-tuples of points in P2(k) both from a theoretical and computational point of view. In particular the case of 8-tuples, corresponding to Del Pezzo surfaces of degree 1, will be the one around which most of the work will revolve, culminating with the statement of a degree 8 monic polynomial expressing the number of 888-tuples of points in general position as a function of the dimension of the base field. The work concludes by con...
This thesis will focus on the study of the relationship that exists between Del Pezzo surfaces, a... more This thesis will focus on the study of the relationship that exists between Del Pezzo surfaces, a kind of surface defined as "a smooth birationally trivial surface V on which the anticanonical sheaf is ample" and counting points in the projective plane P2(k) built over a finite field k. The result allowing us to to link the two concepts says that a Del Pezzo surface of degree d bigger that 1 is isomorphic to the blowup up of 9-d points in P2(k). Once we have settled the relationship between the two concepts the results will revolve around counting n-tuples of points in P2(k) both from a theoretical and computational point of view. In particular the case of 8-tuples, corresponding to Del Pezzo surfaces of degree 1, will be the one around which most of the work will revolve, culminating with the statement of a degree 8 monic polynomial expressing the number of 888-tuples of points in general position as a function of the dimension of the base field. The work concludes by con...