Towards the generalized Shapiro and Shapiro conjecture

Details Towards the generalized Shapiro and Shapiro conjecture Towards the generalized Shapiro and Shapiro conjecture

2008-07-13

arxiv.org/abs/0807.2044v1

Mathematics

Algebraic Geometry

Scientific paper

We find a new, asymptotically better, bound $g\le\frac14d^2+O(d)$ 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).

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