Weighted projective space

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In algebraic geometry, a weighted projective spaceP(a0,...,an) is the projective variety Proj(k[x0,...,xn]) associated to the graded ring k[x0,...,xn] where the variable xk has degree ak.

Properties

References

  1. M. Rossi and L. Terracini, Linear algebra and toric data of weighted projective spaces. Rend. Semin. Mat. Univ. Politec. Torino 70 (2012), no. 4, 469--495, proposition 8
  2. This should be understood as a GIT quotient. In a more general setting, one can speak of a weighted projective stack. See https://mathoverflow.net/questions/136888/.