Supriya Ghosh (Editor)

Segre surface

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In algebraic geometry, a Segre surface, studied by Corrado Segre (1884) and Beniamino Segre (1951), is an intersection of two quadrics in 4-dimensional projective space. They are rational surfaces isomorphic to a projective plane blown up in 5 points with no 3 on a line, and are del Pezzo surfaces of degree 4, and have 16 rational lines. The term "Segre surface" is also occasionally used for various other surfaces, such as a quadric in 3-dimensional projective space, or the hypersurface

x 1 x 2 x 3 + x 2 x 3 x 4 + x 3 x 4 x 5 + x 4 x 5 x 1 + x 5 x 1 x 2 = 0.

References

Segre surface Wikipedia