Real Algebraic and Analytic Geometry |

Asymptotically maximal families of hypersurfaces in toric varieties.

e-mail:

Submission: 2005, January 25.

*Abstract:
A real algebraic variety is maximal (with respect to the Smith Thom
inequality) if the sum of the Betti numbers (with $\mathbb{Z}_2$
coefficients) of the real part of the variety is equal to the sum of
Betti numbers of its complex part. We prove that there exist
polytopes that are not Newton polytopes of any maximal hypersurface
in the corresponding toric variety. On the other hand we show that
for any polytope $\Delta$ there are families of hypersurfaces with
the Newton polytopes $(\lambda\Delta )_{\lambda \in \mathbb{N}}$
that are asymptotically maximal when $\lambda$ tends to infinity.
We also show that these results generalize to complete
intersections
.*

Mathematics Subject Classification (2000): 14P25.

Keywords and Phrases: Viro method, combinatorial patchworking, toric varieties.

**Full text**, 18p.:
dvi 105k,
ps.gz 205k,
pdf 257k.

Server Home Page