Towards the generalized Shapiro and Shapiro conjecture

Abstract

We find a new, asymptotically better, bound $g\le \frac{1}{4}{d}^2+O(d)$ on the genus of a curve that may violate the generalized total reality conjecture. The bound covers all known cases except $g=0$ (the original conjecture).

References in corpus (1)

• The B. and M. Shapiro conjecture in real algebraic geometry and the Bethe ansatz