## 3. Invariants

From a differential geometry perspective we can assign invariants to a smooth curve or surface. This allows us to assign a signature curve to each curve.-
#### Problem 3.1.

How complete are these invariants? If two curves have the same signature what can we say about them? -
#### Problem 3.2.

What can we say about the degree of a signature curve? How is it related to the automorphism group of the original curve? -
#### Problem 3.6.

Can we use differential (integral, otherâ€¦) invariants to construct a moduli space? -
#### Problem 3.8.

Find local invariants for a natural (Lie) groupoid action. (e.g. bathroom tiles in an irregular bathroom). How is this related to quasi-invariants?

Cite this as: *AimPL: Algebraic vision, available at http://aimpl.org/algvision.
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