TY - JOUR
T1 - Convex pencils of real quadratic forms
JF - Discrete and Computational Geometry, Volume 48, Issue 4, December 2012, Pages 1025-1047
Y1 - 2012
A1 - Antonio Lerario
AB - We study the topology of the set X of the solutions of a system of two quadratic inequalities in the real projective space RP^n (e.g. X is the intersection of two real quadrics). We give explicit formulae for its Betti numbers and for those of its double cover in the sphere S^n; we also give similar formulae for level sets of homogeneous quadratic maps to the plane. We discuss some applications of these results, especially in classical convexity theory. We prove the sharp bound b(X)\leq 2n for the total Betti number of X; we show that for odd n this bound is attained only by a singular X. In the nondegenerate case we also prove the bound on each specific Betti number b_k(X)\leq 2(k+2).
PB - Springer
UR - http://hdl.handle.net/1963/7099
N1 - Updated version to be published in DCG ; was published in : Discrete and Computational Geometry, Volume 48, Issue 4, December 2012, Pages 1025-1047
U1 - 7097
U2 - Mathematics
U4 - 1
ER -