Hi,

I am looking for references on theta characteristics. In particular I am interesting in understanding the isomorphism $\Omega_A^g\cong\mathcal{O}_A(\Theta)^2$ where $A$ is an abelian variety and $\Theta$ is the theta divisor. What is the geometric meaning/relation in the case in which $A$ is the Jacobian of a curve $C$ and $\Theta$ is induced by the "canonical" divisor $W^{g-1}$ image of $Pic^{g-1}(X)$? I mean $\Omega_A^g\cong\wedge^g H^0(X,\omega_X)\otimes\mathcal{O}$, so where I "read " "quadratic" theta functions on the differentials??

Thx