We analyze cohomological properties of the Krichever map and use the results to study Weierstrass cycles in moduli spaces and the tautological ring. Let us consider a point p on a smooth projective connected curve C over C of genus g. We say that a natural number n is a non-gap if there exists a function that is holomorphic on C \p and has a pole of order n at the point p (in other words h0(O(n...

Given an algebraically closed field K of characteristic zero, we present the Abhyankar–Jung theorem for any excellent henselian ring whose completion is a formal power series ring K[[z]]. In particular, examples include the local rings which form a Weierstrass system over the field K. The Abhyankar–Jung theorem may be regarded as a higher dimensional counterpart of the Newton–Puiseux theorem. I...