%0 Journal Article
%J Calculus of Variations and Partial Differential Equations
%D 2017
%T Homotopically invisible singular curves
%A Andrei A. Agrachev
%A Francesco Boarotto
%A Antonio Lerario
%B Calculus of Variations and Partial Differential Equations
%V 56
%P 105
%8 Jul
%G eng
%U https://doi.org/10.1007/s00526-017-1203-z
%R 10.1007/s00526-017-1203-z
%0 Journal Article
%J Communications in Analysis and Geometry
%D 2017
%T Homotopy properties of horizontal path spaces and a theorem of Serre in subriemannian geometry
%A Francesco Boarotto
%A Antonio Lerario
%B Communications in Analysis and Geometry
%I International Press of Boston
%V 25
%P 269–301
%G eng
%R 10.4310/CAG.2017.v25.n2.a1
%0 Thesis
%D 2011
%T Homology invariants of quadratic maps
%A Antonio Lerario
%X Given a real projective algebraic set X we could hope that the equations describing it can give some information on its topology, e.g. on the number of its connected components. Unfortunately in the general case this hope is too vague and there is no direct way to extract such information from the algebraic description of X: Even the problem to decide whether X is empty or not is far from an easy visualization and requires some complicated algebraic machinery. A fi rst step observation is that as long as we are interested only in the topology of X, we can replace, using some Veronese embedding, the original ambient space with a much bigger RPn and assume that X is cut by quadratic equations. The price for this is the increase of the number of equations de ning our set; the advantage is that quadratic polynomials are easier to handle and our hope becomes more concrete...
%I SISSA
%G en
%U http://hdl.handle.net/1963/6245
%1 6145
%2 Mathematics
%3 Mathematical Physics
%4 -1
%$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-09-14T09:24:43Z\\nNo. of bitstreams: 1\\nPhd_Thesis_Lerario_Antonio.pdf: 937331 bytes, checksum: f34eea56b610434e63b6f3dd1dded09c (MD5)
%] 1 Basic theory. 2 Nondegeneracy conditions. 3 Spectral sequences. 4 Complex theory. 5 Applications and examples