  An algebro-geometric approach to representations of Sklyanin algebra is
proposed. To each 2 \times 2 quantum L-operator an algebraic curve
parametrizing its possible vacuum states is associated. This curve is called
the vacuum curve of the L-operator. An explicit description of the vacuum curve
for quantum L-operators of the integrable spin chain of XYZ type with arbitrary
spin $\ell$ is given. The curve is highly reducible. For half-integer $\ell$ it
splits into $\ell +{1/2}$ components isomorphic to an elliptic curve. For
integer $\ell$ it splits into $\ell$ elliptic components and one rational
component. The action of elements of the L-operator to functions on the vacuum
curve leads to a new realization of the Sklyanin algebra by difference
operators in two variables restricted to an invariant functional subspace.
