Extremal Real Algebraic Geometry and A-Discriminants Institutional Repository Document uri icon


  • We present a new, far simpler family of counter-examples to Kushnirenko's Conjecture. Along the way, we illustrate a computer-assisted approach to finding sparse polynomial systems with maximally many real roots, thus shedding light on the nature of optimal upper bounds in real fewnomial theory. We use a powerful recent formula for the A-discriminant, and give new bounds on the topology of certain A-discriminant varieties. A consequence of the latter result is a new upper bound on the number of topological types of certain real algebraic sets defined by sparse polynomial equations, e.g., the number of smooth topological types attainable in certain families of real algebraic surfaces.

author list (cited authors)

  • Dickenstein, A., Rojas, J. M., Rusek, K., & Shih, J.

complete list of authors

  • Dickenstein, Alicia||Rojas, J Maurice||Rusek, Korben||Shih, Justin

Book Title

  • arXiv

publication date

  • September 2006