@article{3e052e6a3d684c459292c32561c90304,
title = "Enumeration of complex and real surfaces via tropical geometry",
abstract = "We prove a correspondence theorem for singular tropical surfaces in 3, which recovers singular algebraic surfaces in an appropriate toric three-fold that tropicalize to a given singular tropical surface. Furthermore, we develop a three-dimensional version of Mikhalkin's lattice path algorithm that enumerates singular tropical surfaces passing through an appropriate configuration of points in 3. As application we show that there are pencils of real surfaces of degree d in 3 containing at least (3/2)d3 + O(d2) singular surfaces, which is asymptotically comparable to the number 4(d - 1)3 of all complex singular surfaces in the pencil. Our result relies on the classification of singular tropical surfaces [12].",
keywords = "Tropical geometry, discriminants, real singular surfaces, tropical singular surface",
author = "Hannah Markwig and Thomas Markwig and Eugenii Shustin",
note = "Publisher Copyright: {\textcopyright} 2018 Walter de Gruyter GmbH, Berlin/Boston 2018.",
year = "2018",
month = jan,
day = "1",
doi = "10.1515/advgeom-2017-0024",
language = "אנגלית",
volume = "18",
pages = "69--100",
journal = "Advances in Geometry",
issn = "1615-715X",
publisher = "Walter de Gruyter GmbH",
number = "1",
}