Geodesic
Patching formulas for spin polynomials, and a~proof of the Van de Ven conjecture
Izvestiya. Mathematics , Tome 45 (1995) no. 3, pp. 529-543.

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In the present paper some formulas for spin invariants of a connected sum of an arbitrary four-dimensional manifold $X$ with $b_2^+(X)>0$ and $\overline{\mathbb C\mathbb P^2}$ in terms of spin invariants of $X$ are obtained, and the results are used to get a proof of the Van de Ven conjecture. 
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V. Ya. Pidstrigach. Patching formulas for spin polynomials, and a~proof of the Van de Ven conjecture. Izvestiya. Mathematics , Tome 45 (1995) no. 3, pp. 529-543. http://geodesic.mathdoc.fr/item/IM2_1995_45_3_a4/

[1] S. Bauer, V. Pidstrigatch, “Spin polynomial invariants for Dolgachev survaces”, Israel Math. Conf. Proc., 9, Bar-Ilan Univ., Ramat Gan, 1996, 49–73 | MR | Zbl

[2] S. Donaldson, “Polynomial invariants for smooth four-manifolds”, Topology, 29 (1990), 257–315 | DOI | MR | Zbl

[3] S. Donaldson, P. Kronheimer, The geometry of four-manifolds, Oxford Mathematical Monographs, Oxford University Press, 1990 | MR | Zbl

[4] R. Friedman, J. W. Morgan, “On the diffeomorphism types of certain algebraic surfaces. I”, J. Diff. Geom., 27 (1988), 297–369 | MR | Zbl

[5] R. Friedman, Z. Qin, “The smooth in variance of the Kodaira dimension of a complex surface”, Mathematical Research Letters, 1 (1994), 369–376 | MR | Zbl

[6] R. Friedman, Z. Qin, “On complex surfaces diffeomorphic to rational surfaces”, Invent. Math., 120:1 (1995), 81–117 | DOI | MR | Zbl

[7] N. J. Hitchin, “Harmonic spinors”, Advances in Math., 14 (1974), 1–54 | DOI | MR

[8] D. Kotschick, “On manifolds homeomorphic to $C\mathrm P^2\#8\overline{C\mathrm P}^2$”, Invent. Math., 95 (1989), 591–600 | DOI | MR | Zbl

[9] J. Morgan, T. Mrowka, “A note on Donaldson's polynomial invariants”, Int. Math. Research Notices, 10 (1992), 222–230

[10] C. Okonek, A. Van de Ven, “$\Gamma$-invariants associated to $PU(2)$-bundles and the differentiable structure of Barlow surface”, Invent. Math., 95 (1989), 601–614 | DOI | MR | Zbl

[11] V. Ya. Pidstrigach, “Deformatsiya instantonnykh poverkhnostei”, Izv. AN. Ser. matem., 55:2 (1991), 318–338 | MR | Zbl

[12] V. Ya. Pidstrigach, A. N. Tyurin, “Invarianty gladkoi struktury algebraicheskoi poverkhnosti, zadavaemye operatorom Diraka”, Izv. AN. Ser. matem., 56:2 (1992), 279–371 | MR | Zbl

[13] A. N. Tyurin, “Spin-polinomialnye invarianty gladkikh struktur na algebraicheskikh poverkhnostyakh”, Izv. AN. Ser. matem., 57:2 (1993), 125–164 | MR | Zbl

[14] Z. Qin, “Complex structures on certain differentiable 4-manifolds”, Topology, 32 (1993), 551–566 | DOI | MR | Zbl

[15] Z. Qin, “On smooth structures of potential surfaces of general type homeomorphic to rational surfaces”, Invent. Math., 113 (1993), 163–175 | DOI | MR | Zbl

[16] A. Van de Ven, “On the differentiable structure of certain algebraic surfaces”, Sem. Bourbaki, 667, 1986 | MR | Zbl