Ampleness of intersections of translates of theta divisors in an abelian   fourfold
  We prove that the cotangent bundle of a complete intersection of two general translates of the theta divisor of the jacobian of a general curve of genus 4 is ample. From this the same result for a general principally polarized abelian variety of dimension 4 follows. 
O. Debarre and E. Izadi