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Список литературы
|
|
| |
| 1. |
C. Bănică, N. Manolache, “Rank 2 stable vector bundles on $\mathbb{P}^3(\mathbb{C})$ with Chern classes $c_1=-1$, $c_2 = -4$”, Math. Z., 190:3 (1985), 315–339    |
| 2. |
C. Bănică, M. Putinar, G. Schumacher, “Variation der globalen Ext in Deformationen kompakter komplexer Räume”, Math. Ann., 250:2 (1980), 135–155 |
| 3. |
W. Barth, “Some properties of stable rank-2 vector bundles on $\mathbb{P}_n$”, Math. Ann., 226:2 (1977), 125–150 |
| 4. |
W. Barth, “Stable vector bundles on $\mathbb{P}_3$, some experimental data”, Les équations de Yang–Mills, Seminaire E.N.S. 1977–1978, Astérisque, 71-72, Soc. Math. France, Paris, 1980, 205–218 |
| 5. |
W. Barth, G. Elencwajg, “Concernant la cohomologie des fibres algébriques stables sur $\mathbb{P}_n(\mathbb{C})$”, Variétés analytiques compactes (Nice, 1977), Lecture Notes in Math., 683, Springer, Berlin, 1978, 1–24 |
| 6. |
W. Barth, K. Hulek, “Monads and moduli of vector bundles”, Manuscripta Math., 25:4 (1978), 323–347 |
| 7. |
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. |
| 8. |
G. Bohnhorst, H. Spindler, “The stability of certain vector bundles on $\mathbb{P}^n$”, Complex algebraic varieties (Bayreuth, 1990), Lecture Notes in Math., 1507, Springer, Berlin, 1992, 39–50 |
| 9. |
J. Brun, A. Hirschowitz, “Variété des droites sauteuses du fibré instanton général”, Compos. Math., 53:3 (1984), 325–336 |
| 10. |
U. Bruzzo, D. Markushevich, A. S. Tikhomirov, “Moduli of symplectic instanton vector bundles of higher rank on projective space $\mathbb{P}^3$”, Cent. Eur. J. Math., 10:4 (2012), 1232–1245 |
| 11. |
Mei-Chu Chang, “Stable rank 2 bundles on $\mathbf{IP}^3$ with $c_1=0$, $c_2=4$ and $\alpha=1$”, Math. Z., 184:3 (1983), 407–415 |
| 12. |
Mei-Chu Chang, “Stable rank 2 reflexive sheaves on $\mathbf{P}^3$ with small $c_2$ and applications”, Trans. Amer. Math. Soc., 284:1 (1984), 57–89 |
| 13. |
I. Coandă, A. Tikhomirov, G. Trautmann, “Irreducibility and smoothness of the moduli space of mathematical 5-instantons over $\mathbb{P}_3$”, Internat. J. Math., 14:1 (2003), 1–45 |
| 14. |
L. Costa, R. M. Miró-Roig, “Monads and regularity of vector bundles on projective varieties”, Michigan Math. J., 55:2 (2007), 417–436 |
| 15. |
L. Ein, “Generalized null correlation bundles”, Nagoya Math. J., 111 (1988), 13–24 |
| 16. |
G. Ellingsrud, S. A. Strømme, “Stable rank $2$ vector bundles on $\mathbb{P}^3$ with $c_1 = 0$ and $c_2 = 3$”, Math. Ann., 255:1 (1981), 123–135 |
| 17. |
B. Fantechi, L. Göttsche, L. Illusie, S. L. Kleiman, N. Nitsure, A. Vistoli, Fundamental algebraic geometry. Grothendieck's FGA explained, Math. Surveys Monogr., 123, Amer. Math. Soc., Providence, RI, 2005, x+339 pp. |
| 18. |
Р. Хартсхорн, Алгебраическая геометрия, Мир, М., 1981, 600 с. ; пер. с англ.: R. Hartshorne, Algebraic geometry, Grad. Texts in Math., 52, Springer-Verlag, New York–Heidelberg, 1977, xvi+496 с. |
| 19. |
R. Hartshorne, “Stable vector bundles of rank 2 on $\mathbb{P}^3$”, Math. Ann., 238:3 (1978), 229–280 |
| 20. |
R. Hartshorne, “Stable reflexive sheaves”, Math. Ann., 254:2 (1980), 121–176 |
| 21. |
R. Hartshorne, A. P. Rao, “Spectra and monads of stable bundles”, J. Math. Kyoto Univ., 31:3 (1991), 789–806 |
| 22. |
R. Hartshorne, I. Sols, “Stable rank 2 vector bundles on $\mathbf{P}^3$ with $c_1=-1$, $c_2=2$”, J. Reine Angew. Math., 325 (1981), 145–152 |
| 23. |
G. Horrocks, “Vector bundles on the punctured spectrum of a local ring”, Proc. London Math. Soc. (3), 14:4 (1964), 689–713 |
| 24. |
D. Huybrechts, M. Lehn, The geometry of moduli spaces of sheaves, Cambridge Math. Lib., 2nd ed., Cambridge, Cambridge Univ. Press, 2010, xviii+325 pp. |
| 25. |
M. Jardim, “Instanton sheaves on complex projective spaces”, Collect. Math., 57:1 (2006), 69–91 |
| 26. |
M. Jardim, S. Marchesi, A. Wissdorf, “Moduli of autodual instanton bundles”, Bull. Braz. Math. Soc. (N.S.), 47:3 (2016), 823–843 |
| 27. |
M. Jardim, R. V. Martins, “Linear and Steiner bundles on projective varieties”, Comm. Algebra, 38:6 (2010), 2249–2270 |
| 28. |
M. Jardim, M. Verbitsky, “Trihyperkähler reduction and instanton bundles on $\mathbb{C}\mathbb{P}^3$”, Compos. Math., 150:11 (2014), 1836–1868 |
| 29. |
P. I. Katsylo, “Rationality of the module variety of mathematical instantons with $c_2=5$”, Lie groups, their discrete subgroups, and invariant theory, Adv. Soviet Math., 8, Amer. Math. Soc., Providence, RI, 1992, 105–111 |
| 30. |
P. I. Katsylo, G. Ottaviani, “Regularity of the moduli space of instanton bundles $\mathbf{MI}_{\mathbf{P}^3}(5)$”, Transform. Groups, 8:2 (2003), 147–158 |
| 31. |
A. A. Kytmanov, A. S. Tikhomirov, S. A. Tikhomirov, “Series of rational moduli components of stable rank two vector bundles on $\mathbb{P}^3$”, Selecta Math. (N.S.), 25:2 (2019), 29, 47 pp. |
| 32. |
H. Lange, “Universal families of extensions”, J. Algebra, 83:1 (1983), 101–112 |
| 33. |
N. Manolache, “Rank 2 stable vector bundles on $\mathbf{P}^3$ with Chern classes $c_1=-1$, $c_2=2$”, Rev. Roumaine Math. Pures Appl., 26:9 (1981), 1203–1209 |
| 34. |
M. Maruyama, “Moduli of stable sheaves. I”, J. Math. Kyoto Univ., 17:1 (1977), 91–126 |
| 35. |
К. Оконек, М. Шнейдер, Х. Шпиндлер, Векторные расслоения на комплексных проективных пространствах, Мир, М., 1984, 312 с. ; пер. с англ.: Ch. Okonek, M. Schneider, H. Spindler, Vector bundles on complex projective spaces, Progr. Math., 3, Birkhäuser, Boston, Mass., 1980, vii+389 с. |
| 36. |
A. P. Rao, “A family of vector bundles on $\mathbb{P}^3$”, Space curves (Rocca di Papa, 1985), Lecture Notes in Math., 1266, Springer, Berlin, 1987, 208–231 |
| 37. |
И. Р. Шафаревич, “Ч. 1. Основные понятия”, Основы алгебраической геометрии, 3-е изд., доп., МЦНМО, М., 2007, 13–306; англ. пер.: I. R. Shafarevich, Basic algebraic geometry, т. 1, Varieties in projective space, 3rd ed., Springer, Heidelberg, 2013, xviii+310 с. |
| 38. |
А. С. Тихомиров, “Модули математических инстантонных векторных расслоений с нечетным $c_2$ на проективном пространстве”, Изв. РАН. Сер. матем., 76:5 (2012), 143–224  ; англ. пер.: A. S. Tikhomirov, “Moduli of mathematical instanton vector bundles with odd $c_2$ on projective space”, Izv. Math., 76:5 (2012), 991–1073 |
| 39. |
А. С. Тихомиров, “Модули математических инстантонных векторных расслоений с четным $c_2$ на проективном пространстве”, Изв. РАН. Сер. матем., 77:6 (2013), 139–168 ; англ. пер.: A. S. Tikhomirov, “Moduli of mathematical instanton vector bundles with even $c_2$ on projective space”, Izv. Math., 77:6 (2013), 1195–1223  |
| 40. |
А. С. Тихомиров, С. А. Тихомиров, Д. А. Васильев, “Построение стабильных расслоений ранга $2$ на ${\mathbb P}^3$ посредством симплектических расслоений”, Сиб. матем. журн., 60:2 (2019), 441–460 ; англ. пер.: A. S. Tikhomirov, S. A. Tikhomirov, D. A. Vassiliev, “Construction of stable rank 2 bundles on $\mathbb{P}^3$ via symplectic bundles”, Siberian Math. J., 60:2 (2019), 343–358 |
