On the enumerative geometry of real algebraic curves having many real branches

Abstract

Let C be a smooth real plane curve. Let c be its degree and g its genus. We assume that C has at least g real branches. Let d be a nonzero natural integer strictly less than c. Let e be a partition of cd of length g. Let n be the number of all real plane curves of degree d that are tangent to g real branches of C with orders of tangency e1; .. .; eg. We show that n is finite and we determine n explicitly.