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Izv. RAN. Ser. Mat., 1992, Volume 56, Issue 2, Pages 279–371 (Mi izv947)  

This article is cited in 13 scientific papers (total in 14 papers)

Invariants of the smooth structure of an algebraic surface arising from the Dirac operator

V. Ya. Pidstrigach, A. N. Tyurin

Abstract: We construct invariants of the smooth structure of an algebraic surface in terms of coupled Dirac operators. The invariants allow us to distinguish between del Pezzo surfaces and fake del Pezzo surfaces by their smooth structure.

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English version:
Russian Academy of Sciences. Izvestiya Mathematics, 1993, 40:2, 267–351

Bibliographic databases:

UDC: 516.5
MSC: Primary 14J99, 57N13; Secondary 14J25
Received: 25.06.1991

Citation: V. Ya. Pidstrigach, A. N. Tyurin, “Invariants of the smooth structure of an algebraic surface arising from the Dirac operator”, Izv. RAN. Ser. Mat., 56:2 (1992), 279–371; Russian Acad. Sci. Izv. Math., 40:2 (1993), 267–351

Citation in format AMSBIB
\by V.~Ya.~Pidstrigach, A.~N.~Tyurin
\paper Invariants of the smooth structure of an algebraic surface arising from the Dirac operator
\jour Izv. RAN. Ser. Mat.
\yr 1992
\vol 56
\issue 2
\pages 279--371
\jour Russian Acad. Sci. Izv. Math.
\yr 1993
\vol 40
\issue 2
\pages 267--351

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    This publication is cited in the following articles:
    1. T. L. Troshina, “The degree of the top Segre class of the standard vector bundle on the Hilbert scheme $\operatorname{Hilb}^4S$ of an algebraic surface $S$”, Russian Acad. Sci. Izv. Math., 43:3 (1994), 493–516  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. A. N. Tyurin, “Spin polynomial invariants of smooth structures on algebraic surfaces”, Russian Acad. Sci. Izv. Math., 42:2 (1994), 333–369  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. V. Ya. Pidstrigach, “Patching formulas for spin polynomials, and a proof of the Van de Ven conjecture”, Russian Acad. Sci. Izv. Math., 45:3 (1995), 529–543  mathnet  crossref  mathscinet  zmath  isi
    4. A. N. Tyurin, “Canonical spin polynomials of an algebraic surface. I”, Russian Acad. Sci. Izv. Math., 45:3 (1995), 577–621  mathnet  crossref  mathscinet  zmath  isi
    5. Christian Okonek, Andrei Teleman, “Quaternionic monopoles”, Comm Math Phys, 180:2 (1996), 363  crossref  mathscinet  zmath  isi
    6. N. A. Tyurin, “Necessary and sufficient conditions for a deformation of a B-monopole into an instanton”, Izv. Math., 60:1 (1996), 217–230  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. B. V. Karpov, “On the algebraic geometry of $S$-duality”, Math. Notes, 61:2 (1997), 133–145  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. Paul M.N. Feehan, Thomas G. Leness, “PU(2) monopoles and relations between four-manifold invariants”, Topology and its Applications, 88:1-2 (1998), 111  crossref
    9. B. V. Karpov, “$S$-duality testing and exceptional bundles”, Izv. Math., 63:1 (1999), 103–117  mathnet  crossref  crossref  mathscinet  zmath  isi
    10. A. N. Tyurin, “Special Lagrangian geometry as slightly deformed algebraic geometry (geometric quantization and mirror symmetry)”, Izv. Math., 64:2 (2000), 363–437  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    11. N. A. Tyurin, “Instantons and monopoles”, Russian Math. Surveys, 57:2 (2002), 305–360  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    12. F. A. Bogomolov, A. L. Gorodentsev, V. A. Iskovskikh, Yu. I. Manin, V. V. Nikulin, D. O. Orlov, A. N. Parshin, V. Ya. Pidstrigach, A. S. Tikhomirov, N. A. Tyurin, I. R. Shafarevich, “Andrei Nikolaevich Tyurin (obituary)”, Russian Math. Surveys, 58:3 (2003), 597–605  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    13. Kai Cieliebak, Ignasi Mundet i Riera, Dietmar A. Salamon, “Equivariant moduli problems, branched manifolds, and the Euler class”, Topology, 42:3 (2003), 641  crossref
    14. V. Ya. Pidstrigach, “Hyperkähler Manifolds and Seiberg–Witten Equations”, Proc. Steklov Inst. Math., 246 (2004), 249–262  mathnet  mathscinet  zmath
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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