E. Arrondo and I. , Sols On conguences of lines in projective space, Mémoires de la S.M.F. 2 a série, 1992.

K. Aström and F. , Kahl Ambiguous Configurations for the 1D Structure and Motion Problem, Journal of Mathematical Imaging and Vision, vol.18, issue.2, pp.191-203, 2003.
DOI : 10.1023/A:1022120702016

M. Bertolini, G. Besana, and C. Turrini, Instability of Projective Reconstruction of Dynamic Scenes near Critical Configurations, 2007 IEEE 11th International Conference on Computer Vision, 2007.
DOI : 10.1109/ICCV.2007.4409100

M. Bertolini, G. Besana, and C. Turrini, Instability of projective reconstruction from 1-view near critical configurations in higher dimensions, Algebra Geometry and their Interactions, 2007.
DOI : 10.1090/conm/448/08654

M. Bertolini, G. Besana, and C. Turrini, Reconstruction of Some Segmented and Dynamic Scenes: Trifocal Tensors in ???4 Theoretical Set Up for Critical Loci, and Instability, Advances in Visual Computing , Proceedings of the International Symposium on Visual Computing, 2008.
DOI : 10.1007/978-1-4757-5323-3

M. Bertolini, G. Besana, C. Turrini-aja-fernndez, S. De, L. Garcia et al., Applications Of Multiview Tensors In Higher Dimensions in " Tensors in Image Processing and Computer Vision Advances in Pattern Recognition, 2009.

M. Bertolini, G. Besana, and C. Turrini, Critical loci for projective reconstruction from multiple views in higher dimension: A comprehensive theoretical approach, Linear Algebra and its Applications, vol.469, pp.469-335, 2015.
DOI : 10.1016/j.laa.2014.11.021

M. Bertolini, G. Besana, and C. Turrini, Generalized Fundamental Matrices as, pp.196-539, 2017.
DOI : 10.1007/s10231-016-0585-4

M. Bertolini, G. Besana, R. Notari, and C. Turrini, Provisional title: Critical loci for 3?view reconstruction in P 4 : the degenerate cases and instability

M. Bertolini and L. Magri, Critical hypersurfaces and instability for reconstruction of scenes in high dimensional projective spaces, 2017.
DOI : 10.1109/iccv.2007.4409100

M. Bertolini and C. Turrini, Critical Configurations for 1-View in Projections from ???k ??? ???2, Journal of Mathematical Imaging and Vision, vol.48, issue.1, 2007.
DOI : 10.1007/s10851-007-0649-6

G. Bordiga, La superficie del 6 ? ordine con 10 rette, nello spazio R 4 e le sue proiezioni nello spazio ordinario, Mem.Accad.Lincei, vol.3, issue.4, pp.182-203, 1887.

T. Buchanan, The twisted cubic and camera calibration. Comput. Vision Graphics Image Process, pp.130-132, 1988.
DOI : 10.1016/0734-189x(88)90024-2

URL : http://elib.uni-stuttgart.de/bitstream/11682/7175/1/bu8.pdf

T. Buchanan, On the critical set for photogrammetric reconstruction using line tokens in P 3(?), Geometriae Dedicata, vol.44, issue.2, pp.223-232, 1992.
DOI : 10.1007/BF00182950

W. Decker, G. M. Greuel, G. Pfister, and H. Schönemann, Singular 4-1-0 ? A computer algebra system for polynomial computations, 2016.

I. V. Dolgachev, Classical Algebraic Geometry. A modern view, 2012.

D. Eisenbud, Commutative Algebra. Graduate Texts in Mathematics 150, 1999.

G. Ellingsrud, Sur le sch??ma de Hilbert des vari??t??s de codimension $2$ dans $\mathbf{P}^e$ ?? c??ne de Cohen-Macaulay, Annales scientifiques de l'??cole normale sup??rieure, vol.8, issue.4, pp.423-431, 1975.
DOI : 10.24033/asens.1297

URL : http://www.numdam.org/article/ASENS_1975_4_8_4_423_0.pdf

R. I. Hartley, Ambiguous Configurations for 3-View Projective Reconstruction, European Conference on Computer Vision, pp.922-935, 2000.
DOI : 10.1007/3-540-45054-8_60

URL : http://rsise.anu.edu.au/~hartley/Papers/3view-degeneracies/3view-degeneracies.pdf

R. I. Hartley and F. Kahl, Critical Configurations for Projective Reconstruction from Multiple Views, International Journal of Computer Vision, vol.49, issue.2, pp.5-47, 2007.
DOI : 10.1007/978-3-642-77557-4

R. I. Hartley and F. Schaffalitzky, Reconstruction from projections using Grassmann tensors, Proceedings of the 8th European Conference on Computer Vision, 2004.
DOI : 10.1007/s11263-009-0225-1

R. Hartley and R. Vidal, The multibody trifocal tensor: motion segmentation from 3 perspective views, Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004., 2004.
DOI : 10.1109/CVPR.2004.1315109

URL : http://www.cis.jhu.edu/~rvidal/publications/cvpr04-trifocal-final.pdf

R. I. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision, 2004.
DOI : 10.1017/CBO9780511811685

F. Kahl, R. Hartley, and K. Aström, Critical configurations for n-view projective reconstruction, Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001, pp.158-163, 2001.
DOI : 10.1109/CVPR.2001.990945

URL : http://www.maths.lth.se/matematiklth/personal/fredrik/cvpr01short_hartley.ps

J. O. Kleppe, J. C. Migliore, R. Miró, ?. Roig, U. Nagel et al., Gorenstein Liaison, Complete Intersection Liaison Invariants and Onubstructedness, Mem. Amer. Math. Soc, vol.154, p.732, 2001.
DOI : 10.1090/memo/0732

J. Kollár, K. E. Smith, and A. Corti, Rational and nearly rational varieties, In Cambridge Studies in Advanced Mathematics, 2004.

J. Krames, Zur Ermittlung eines Objektes aus zwei Perspektiven. (Ein Beitrag zur Theorie der ???gef??hrlichen ??rter???.), Monatshefte f??r Mathematik und Physik, vol.67, issue.1, pp.327-354, 1940.
DOI : 10.1515/crll.1883.95.1

K. Huang, R. Fossum, and Y. Ma, Generalized Rank Conditions in Multiple View Geometry with Applications to Dynamical Scenes, European Conference on Computer Vision, 2002.
DOI : 10.1007/3-540-47967-8_14

URL : http://black1.csl.uiuc.edu/~yima/psfile/eccv02_paper86.ps

S. J. Maybank, Theory of Reconstruction from Image Motion, 1992.
DOI : 10.1007/978-3-642-77557-4

S. J. Maybank, The critical line congruence for reconstruction from three images, Applicable Algebra in Engineering, Communication and Computing, vol.4, issue.2, pp.89-113, 1995.
DOI : 10.1007/BF01225646

R. Notari and M. L. , A stratification of Hilbert schemes by initial ideals and applications, manuscripta mathematica, vol.101, issue.4, pp.429-448, 2000.
DOI : 10.1007/s002290050225

G. Ottaviani, Varietà proiettive di codimensione piccola, INdAM ? Aracne, 1995.

J. G. Semple and L. Roth, Introduction to Algebraic Geometry, 1949.

J. Shamash, The Poincaré series of a local ring, J. Algebra, vol.12, p.453470, 1969.

A. Shashua and S. J. Maybank, Degenerate n point configurations of three views: Do critical surfaces exist? TR 96-19, 1996.

R. Vidal and Y. Ma, A Unified Algebraic Approach to 2-D and 3-D Motion Segmentation and Estimation, Journal of Mathematical Imaging and Vision, 2006.
DOI : 10.1007/s10851-006-8286-z

R. Vidal, Y. Ma, S. Soatto, and S. Sastry, Two-View Multibody Structure from Motion, International Journal of Computer Vision, vol.27, issue.12, 2006.
DOI : 10.1007/s11263-005-4839-7

URL : http://www.cs.berkeley.edu/~sastry/pubs/Pdfs of 2006/VidalTwo-View2006.pdf

X. Fan and R. Vidal, The Space of Multibody Fundamental Matrices: Rank, Geometry and Projection, Dynamical Vision, 2007.
DOI : 10.1007/978-3-540-70932-9_1

L. Wolf and A. Shashua, On projection matrices P/sup k/???P/sup 2/, k=3,...,6, and their applications in computer vision, Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001, 2002.
DOI : 10.1109/ICCV.2001.937547

S. Verra, Smooth surfaces of degree 9 in G(1, 3) E-mail address: marina.bertolini@unimi.it E-mail address: roberto.notari@polimi.it E-mail address: cristina.turrini@unimi.it Dipartimento di Matematica " F. Enriques, Manuscripta Mathematica Via Saldini, vol.62, issue.50, pp.416-435, 1988.
DOI : 10.1007/bf01357719