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Minimality of the D-groupoid of symmetries of a projective structure
Minimalidad del D-grupoide de simetrías de una estructura proyectiva
Palabras clave:
Schwarzian equation, Schwarzian derivative, Strong minimality, Symmetric Power, Lie groupoid, D-groupoid (en)derivada Schwarziana, fuerte minimalidad, grupoide de Lie, D-grupoide, Ecuación Schwarziana, potencia simétrica (es)
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In this article we study Kummer’s D-groupoid, which is the groupoid of symmetries of a meromorphic projective structure. We give necessary and sufficient conditions for its minimality, in the sense of not having infinite sub-D-groupoids. The condition that we find turns out to be equivalent to the strong minimality of the non-linear Schwarzian equation and the non-integrability by means of Liouvillian functions of the linear Schwarzian equation.
En este artículo estudiamos el D-grupoide de Kummer, el cual es el grupoide de simetrías de una estructura proyectiva meromorfa. Damos condiciones necesarias y suficientes para su simplicidad, en el sentido de no tener sub-D-grupoides no finitos. La condición que encontramos resulta ser equivalente a la fuerte minimalidad de la ecuación schwarziana no lineal y la no integrabilidad mediante funciones liouvillianas de la ecuación schwarziana lineal.
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