44 citations · 138 across the 32 of their papers we have counts for
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Plenty of Morse functions by perturbing with sums of squares
Antonio Lerario
Given a smooth function f on R^n and a submanifold M, we prove that the set of diagonal quadratic forms q such that the restriction of f+q to M is Morse is a dense set (in the n-di…
The total Betti number of the intersection of three real quadrics
Antonio Lerario
We prove that the total Betti number of the intersection X of three quadrics in RP^n is bounded by n(n+1). This bound improves the classical Barvinok's one which is at least of ord…
A real viewpoint on the intersection of complex quadrics and its topology
Antonio Lerario
We study the relation between a complex projective set C in CP^n and the set R in RP^(2n+1) defined by viewing each equation of C as a pair of real equations. Once C is presented b…
Convex pencils of real quadratic forms
Antonio Lerario
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). W…