Toric Euler-Jacobi vanishing theorem and zeros at infinity

Residues in complex manifolds are one of those kind of objects that can be approached both geometrically and algebraically. Their use in computational algebraic geometry is ubiquitous, they appear naturally in interpolation, duality, and several types of representation problems. In this talk, we will review them and their use, and then focus on some vanishing theorems for residues that are well-known classically, and have been extended recently to more general varieties. I will report on joint work with Alicia Dickenstein on the use of residues as witnesses of zeroes at the infinity of toric varieties.