Geodesic
A canonical basis of two-cycles on a $K3$ surface
Sbornik. Mathematics, Tome 209 (2018) no. 8, pp. 1248-1256 Cet article a éte moissonné depuis la source Math-Net.Ru

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We construct a basis of two-cycles on a $K3$ surface; in this basis, the intersection form takes the canonical form $2E_8(-1) \oplus 3H$. Elements of the basis are realized by formal sums of smooth submanifolds. Bibliography: 8 titles.
Keywords: $K3$ surface, intersection form. 
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I. A. Taimanov. A canonical basis of two-cycles on a $K3$ surface. Sbornik. Mathematics, Tome 209 (2018) no. 8, pp. 1248-1256. http://geodesic.mathdoc.fr/item/SM_2018_209_8_a6/

[1] J. W. Milnor, “On simply connected $4$-manifolds”, Symposium internacional de topología algebraica, Universidad Nacional Autónoma de México and UNESCO, Mexico City, 1958, 122–128 | MR | Zbl

[2] J.-P. Serre, A course in arithmetic, Grad. Texts in Math., 7, Springer–Verlag, New York–Heidelberg, 1973, viii+115 pp. | DOI | MR | MR | Zbl | Zbl

[3] I. R. Shafarevich, B. G. Averbukh, Yu. R. Vainberg, A. B. Zhizhchenko, Yu. I. Manin, B. G. Moishezon, G. N. Tyurina, A. N. Tyurin, “Algebraicheskie poverkhnosti”, Tr. MIAN SSSR, 75, Nauka, M., 1965, 3–215 | MR | Zbl

[4] W. P. Barth, K. Hulek, C. A. M. Peters, A. Van de Ven, Compact complex surfaces, Ergeb. Math. Grenzgeb. (3), 4, 2nd ed., Springer-Verlag, Berlin, 2004, xii+436 pp. | DOI | MR | Zbl

[5] D. Huybrechts, Lectures on K3 surfaces, Cambridge Stud. Adv. Math., 158, Cambridge Univ. Press, Cambridge, 2016, xi+485 pp. | DOI | MR | Zbl

[6] I. I. Pjateckiĭ-Šapiro, I. R. Šafarevič, “A Torelli theorem for algebraic surfaces of type $K3$”, Math. USSR-Izv., 5:3 (1971), 547–588 | DOI | MR | Zbl

[7] E. Spanier, “The homology of Kummer manifolds”, Proc. Amer. Math. Soc., 7:1 (1956), 155–160 | DOI | MR | Zbl

[8] M. Glezerman, L. Pontryagin, “Intersections in manifolds”, Amer. Math. Soc. Transl., 1951, Amer. Math. Soc., Providence, RI, 1951, 50, 149 pp. | MR | MR