What is the total Betti number of a random real hypersurface?
نویسندگان
چکیده
منابع مشابه
What is the total Betti number of a random real hypersurface?
We bound from above the expected total Betti number of a high degree random real hypersurface in a smooth real projective manifold. This upper bound is deduced from the equirepartition of critical points of a real Lefschetz pencil restricted to the complex domain of such a random hypersurface, equirepartition which we first establish. Our proofs involve Hörmander’s theory of peak sections as we...
متن کاملWhat is the Real Cause of Glaucoma?
Introduction: The term glaucoma refers to a group of diseases that have a characteristic optic neuropathy with associated visual field loss in common. Intraocular pressure has been considered to be the only causal factor for glaucoma and the only factor that can be manipulated to alter the course of the disease. But considering high intraocular pressure as the only factor responsible for glauco...
متن کاملGraph colouring and the total Betti number
The total Betti number of the independence complex of a graph is an intriguing graph invariant. Kalai and Meshulam have raised the question on its relation to cycles and the chromatic number of a graph, and a recent conjecture on that theme was proved by Bonamy, Charbit and Thomassé. We show an upper bound on the total Betti number in terms of the number of vertex disjoint cycles in a graph. Th...
متن کاملL–betti Numbers of Hypersurface Complements
In [DJL07] it was shown that if A is an affine hyperplane arrangement in Cn, then at most one of the L2–Betti numbers b i (C n \ A, id) is non–zero. In this note we prove an analogous statement for complements of complex affine hypersurfaces in general position at infinity. Furthermore, we recast and extend to this higher-dimensional setting results of [FLM09, LM06] about L2–Betti numbers of pl...
متن کاملwhat is the real cause of glaucoma?
introduction: the term glaucoma refers to a group of diseases that have a characteristic optic neuropathy with associated visual field loss in common. intraocular pressure has been considered to be the only causal factor for glaucoma and the only factor that can be manipulated to alter the course of the disease. but considering high intraocular pressure as the only factor responsible for glauco...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal für die reine und angewandte Mathematik (Crelles Journal)
سال: 2014
ISSN: 0075-4102,1435-5345
DOI: 10.1515/crelle-2012-0062