I am interested in the dimension of algebraic stacks.But, I’m in trouble because I can’t calculate it.Are there any good reference or tools for calculating it? I use the “Champs algébriques” by Laumon & Moret - Bailly as a reference for its definition.

Edit:In particular,I want to calculate the dimension of moduli stacks of coherent sheaves and filtered(flag) coherent sheaves.

  • $\begingroup$ Could discussion at mathoverflow.net/questions/275637/dimension-of-artin-stacks be of some help? $\endgroup$ Nov 5, 2019 at 5:18
  • $\begingroup$ Thank you for the comment.I have some questions.I don’t know tangent complex’s(which t3suji said.).Could you tell me tangent complexes or some reference for tangent complexes.And I want to calculate the dimensions in the case of projective surfaces (in the cases ,I don’t know smoothness of the moduli stacks of coherent sheaves even if I only think about torsion-free sheaves.)And I am thinking estimating the dimensions by them of filtered sheaves.Are there any tools to do it? $\endgroup$ Nov 5, 2019 at 5:44


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