Skip to main content
MathOverflow

Return to Question

added 21 characters in body
Source Link
Lya
Lya
  • 63
  • 4

Let S=E\times C$S=E\times C$ be a product of two curves, where E$E$ is an elliptic curve and C$C$ is a curve of genus at least two. Consider a foliation on S$S$ generated by a global holomorphic 1-form p_1^(\omega_1)+p_2^(\omega_2) $p_1^*(\omega_1)+p_2^*(\omega_2)$, where p_i$p_i$ is a projection map and \omega_1$\omega_1$ and \omega_2$\omega_2$ are nonzero holomorphic 1-forms on E$E$ and C$C$ respectively. Is it possible to say something about algebraicity of leaves of this foliation?

Let S=E\times C be a product of two curves, where E is an elliptic curve and C is a curve of genus at least two. Consider a foliation on S generated by a global holomorphic 1-form p_1^(\omega_1)+p_2^(\omega_2), where p_i is a projection map and \omega_1 and \omega_2 are nonzero holomorphic 1-forms on E and C respectively. Is it possible to say something about algebraicity of leaves of this foliation?

Let $S=E\times C$ be a product of two curves, where $E$ is an elliptic curve and $C$ is a curve of genus at least two. Consider a foliation on $S$ generated by a global holomorphic 1-form $p_1^*(\omega_1)+p_2^*(\omega_2)$, where $p_i$ is a projection map and $\omega_1$ and $\omega_2$ are nonzero holomorphic 1-forms on $E$ and $C$ respectively. Is it possible to say something about algebraicity of leaves of this foliation?

Source Link
Lya
Lya
  • 63
  • 4

algebraic leaves of foliation on a product of two curves

Let S=E\times C be a product of two curves, where E is an elliptic curve and C is a curve of genus at least two. Consider a foliation on S generated by a global holomorphic 1-form p_1^(\omega_1)+p_2^(\omega_2), where p_i is a projection map and \omega_1 and \omega_2 are nonzero holomorphic 1-forms on E and C respectively. Is it possible to say something about algebraicity of leaves of this foliation?