@article{ce3979f0c2aa47d38152a8890dc1863b,

title = "Critical points of real polynomials and topology of real algebraic T-surfaces",

abstract = "The paper is devoted to a special class of real polynomials, so-called T-polynomials, which arise in the combinatorial version of the Viro theorem. We study the relation between the numbers of real critical points of a given index of a T-polynomial and the combinatorics of lattice triangulations of Newton polytopes. We obtain upper bounds for the numbers of extrema and saddles of generic T-polynomials of a given degree in three variables, and derive from them upper bounds for Betti numbers of real algebraic surfaces in ℝP 3 defined by T-polynomials. The latter upper bounds are stronger than the known upper bounds for arbitrary real algebraic surfaces in ℝP 3. Another result is the existence of an asymptotically maximal family of real polynomials of degree m in three variables with 31m 3/36 + O(m2) saddle points.",

keywords = "Critical points, Lattice triangulation, Newton polytope, Real algebraic surfaces, Real polynomials",

author = "Ilia Itenberg and Eugenii Shustin",

note = "Funding Information: The main part of this work was done during the authors{\textquoteright} stay in Mathematisches Forschungsinstitut Oberwolfach under the program {\textquoteleft}Research in Pairs{\textquoteright} supported by Volkswagen-Stiftung. The authors are grateful to MFO for the hospitality and excellent working conditions.",

year = "2003",

month = oct,

doi = "10.1023/A:1026321329717",

language = "אנגלית",

volume = "101",

pages = "61--91",

journal = "Geometriae Dedicata",

issn = "0046-5755",

publisher = "Springer Netherlands",

number = "1",

}