Some unlikely intersections between the Torelli locus and Newton strata in Ag

Let p be an odd prime. What are the possible Newton polygons for a curve in characteristic p? Equivalently, which Newton strata intersect the Torelli locus in A(g) ? In this note, we study the Newton polygons of certain curves with Z/pZ-actions. Many of these curves exhibit unlikely intersections between the Torelli locus and the Newton stratification in A(g). Here is one example of particular interest: fix a genus g. We show that for any k with 2g/3 - 2p( p-1)/3 >= 2k(p-1), there exists a curve of genus g whose Newton polygon has slopes {0, 1}(g-k(p-1))coproduct{1/2}(2k(p-1)). This provides evidence for Oort's conjecture that the amalgamation of the Newton polygons of two curves is again the Newton polygon of a curve. We also construct families of curves {C-g}(g >= 1), where C-g is a curve of genus g, whose Newton polygons have interesting asymptotic properties. For example, we construct a family of curves whose Newton polygons are asymptotically bounded below by the graph y = x(2)/4g. The proof uses a Newton-over-Hodge result for Z/pZ-covers of curves due to the author, in addition to recent work of Booher-Pries on the realization of this Hodge bound.