Cohomology of real three-dimensional triquadrics
Izvestiya. Mathematics , Tome 76 (2012) no. 1, pp. 113-138.

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider non-singular intersections of three real five-dimensional quadrics. They are referred to for brevity as real three-dimensional triquadrics. We calculate the dimensions of the cohomology spaces of triquadrics with coefficients in the field of two elements.
Keywords: spectral curve, spectral bundle, index function, theta characteristic.
Mots-clés : triquadric, index scheme, index orientation
@article{IM2_2012_76_1_a4,
     author = {V. A. Krasnov},
     title = {Cohomology of real three-dimensional triquadrics},
     journal = {Izvestiya. Mathematics },
     pages = {113--138},
     publisher = {mathdoc},
     volume = {76},
     number = {1},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2012_76_1_a4/}
}
TY  - JOUR
AU  - V. A. Krasnov
TI  - Cohomology of real three-dimensional triquadrics
JO  - Izvestiya. Mathematics 
PY  - 2012
SP  - 113
EP  - 138
VL  - 76
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2012_76_1_a4/
LA  - en
ID  - IM2_2012_76_1_a4
ER  - 
%0 Journal Article
%A V. A. Krasnov
%T Cohomology of real three-dimensional triquadrics
%J Izvestiya. Mathematics 
%D 2012
%P 113-138
%V 76
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2012_76_1_a4/
%G en
%F IM2_2012_76_1_a4
V. A. Krasnov. Cohomology of real three-dimensional triquadrics. Izvestiya. Mathematics , Tome 76 (2012) no. 1, pp. 113-138. http://geodesic.mathdoc.fr/item/IM2_2012_76_1_a4/

[1] A. Degtyarev, I. Itenberg, V. Kharlamov, On the number of components of a complete intersection of real quadrics, arXiv: 0806.4077v2

[2] O. Ja. Viro, “Curves of degree 7, curves of degree 8, and the Ragsdale conjecture”, Soviet Math. Dokl., 22:2 (1980), 566–570 | MR | Zbl

[3] O. Ja. Viro, “Plane real curves of degrees 7 and 8: New restrictions”, Math. USSR-Izv., 23:2 (1984), 409–422 | DOI | MR | Zbl

[4] A. A. Agrachev, “Topology of quadratic maps and hessians of smooth maps”, J. Soviet Math., 49:3 (1990), 990–1013 | DOI | MR | Zbl

[5] A. C. Dixon, “Note on the reduction of a ternary quantic to a symmetrical determinant”, Proc. Cambridge Philos. Soc., 5 (1902), 350–351 | Zbl

[6] A. N. Tyurin, “On intersections of quadrics”, Russian Math. Surveys, 30:6 (1975), 51–105 | DOI | MR | Zbl | Zbl

[7] I. V. Dolgachev, Topics in classical algebraic geometry. I, www.math.lsa.umich.edu/~idolga/topics.pdf

[8] A. A. Agrachev, “Homology of intersections of real quadrics”, Soviet Math. Dokl., 37:2 (1988), 493–496 | MR | Zbl

[9] V. A. Krasnov, “On the number of components of a three-dimensional maximal intersection of three real quadrics”, Izv. Math., 75:3 (2011), 589–602 | DOI | Zbl

[10] M. F. Atiyah, “Riemann surfaces and spin structures”, Ann. Sci. École Norm. Sup. (4), 4 (1971), 47–62 | MR | Zbl

[11] D. Mumford, “Theta characteristics of an algebraic curve”, Ann. Sci. École Norm. Sup. (4), 4 (1971), 181–192 | MR | Zbl

[12] S. M. Natanzon, Moduli of Riemann surfaces, real algebraic curves, and their superanalogs, Transl. Math. Monogr., 225, Amer. Math. Soc., Providence, RI, 2004 | MR | MR | Zbl | Zbl

[13] Y. I. Manin, “Le groupe de Brauer–Grothendieck en géométrie diophantienne”, Actes du Congrès International des Mathématiciens (Nice, 1970), Ganthcer-Villars, Paris, 1971, 401–411 | MR | Zbl

[14] V. A. Rokhlin, “Complex topological characteristics of real algebraic curves”, Russian Math. Surveys, 33:5 (1978), 85–98 | DOI | MR | Zbl | Zbl

[15] V. Vinnikov, “Self-adjoint determinantal representations of real plane curves”, Math. Ann., 296:3 (1983), 453–479 | DOI | MR | Zbl

[16] E. Brugallé, “Symmetric plane curves of degree 7: pseudoholomorphic and algebraic classifications”, J. Reine Angew. Math., 612 (2007), 129–171 | DOI | MR | Zbl

[17] E. Brugallé, Courbes algébriques réelles et courbes pseudoholomorphes réelles dans les surfaces réglées, /www.math.jussieu.fr/~brugalle/articles/Thesis/These.pdf

[18] V. Florens, “Signatures of colored links with application to real algebraic curves”, J. Knot Theory Ramifications, 14:7 (2005), 883–918 | DOI | MR | Zbl

[19] V. A. Krasnov, “Maximal intersections of three real quadrics”, Izv. Math., 75:3 (2011), 569–587 | DOI | Zbl

[20] M. F. Atiyah, $K$-theory, Benjamin, New York–Amsterdam, 1967 | MR | MR | Zbl | Zbl