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Serge Lvovski
Serge Lvovski
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I am aware of the following examples of normal surfaces in $\mathbb P^3$ that are projectively isomorphic to their dual varieties:

  1. the smooth quadric;

  2. Kummer surfaces;

  3. The surface with the equation $x_0^3=x_1x_2x_3$$x_0^3=x_1x_2x_3$ (in homogeneous coordinates).

What else is known? The base field is algebraically closed of characteristic zero.

Thank you in advance, Serge

I am aware of the following examples of normal surfaces in $\mathbb P^3$ that are projectively isomorphic to their dual varieties:

  1. the smooth quadric;

  2. Kummer surfaces;

  3. The surface with the equation $x_0^3=x_1x_2x_3$ (in homogeneous coordinates).

What else is known? The base field is algebraically closed of characteristic zero.

Thank you in advance, Serge

I am aware of the following examples of normal surfaces in $\mathbb P^3$ that are projectively isomorphic to their dual varieties:

  1. the smooth quadric;

  2. Kummer surfaces;

  3. The surface with the equation $x_0^3=x_1x_2x_3$ (in homogeneous coordinates).

What else is known? The base field is algebraically closed of characteristic zero.

Thank you in advance, Serge

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Serge Lvovski
Serge Lvovski
  • 1.8k
  • 10
  • 14

Self-dual surfaces in $\mathbb P^3$ with isolated singularities

I am aware of the following examples of normal surfaces in $\mathbb P^3$ that are projectively isomorphic to their dual varieties:

  1. the smooth quadric;

  2. Kummer surfaces;

  3. The surface with the equation $x_0^3=x_1x_2x_3$ (in homogeneous coordinates).

What else is known? The base field is algebraically closed of characteristic zero.

Thank you in advance, Serge