Copy For Citation
Kişisel A. U. Ö., Bayraktar T.
27th Gökova GeometryTopology Conference, Muğla, Turkey, 30 May  04 June 2022, pp.1

Publication Type:
Conference Paper / Summary Text

City:
Muğla

Country:
Turkey

Page Numbers:
pp.1

Middle East Technical University Affiliated:
Yes
Abstract
Due to a theorem of Passare and Rullgard, the area of the amoeba of a degree d" role="presentation" >d$d$ algebraic curve in the complex projective plane is bounded above by π2d2/2" role="presentation" >π2d2/2${\pi}^{2}{d}^{2}/2$ and the curves attaining the bound  special Harnack curves  have been characterized by Mikhalkin. In this talk, reporting on joint work with Turgay Bayraktar, I will argue that the expected area of a randomly chosen complex algebraic curve, with respect to the Kostlan distribution, is bounded above by a constant times d" role="presentation" >d$d$. This result also generalizes in a natural way to half dimensional complete intersections in toric varieties with an arbitrary Newton polytope.