The classical Barvinok bound for the sum of the Betti numbers of the intersection X of three quadrics in RPn says that there exists a natural number a such that b(X) <= n(3a). We improve this bound proving the inequality b(X) <= n(n + 1). Moreover we show that this bound is asymptotically sharp as n goes to infinity.

The total Betti number of the intersection of three real quadrics

Lerario, Antonio
2014-01-01

Abstract

The classical Barvinok bound for the sum of the Betti numbers of the intersection X of three quadrics in RPn says that there exists a natural number a such that b(X) <= n(3a). We improve this bound proving the inequality b(X) <= n(n + 1). Moreover we show that this bound is asymptotically sharp as n goes to infinity.
2014
14
3
541
551
https://arxiv.org/abs/1111.3847
Lerario, Antonio
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/32813
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