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.
Citation:
V. Ya. Pidstrigach, A. N. Tyurin, “Invariants of the smooth structure of an algebraic surface arising from the Dirac operator”, Russian Acad. Sci. Izv. Math., 40:2 (1993), 267–351
\Bibitem{PidTyu92}
\by V.~Ya.~Pidstrigach, A.~N.~Tyurin
\paper Invariants of the smooth structure of an algebraic surface arising from the Dirac operator
\jour Russian Acad. Sci. Izv. Math.
\yr 1993
\vol 40
\issue 2
\pages 267--351
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Linking options:
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This publication is cited in the following 19 articles:
Thomas Leness, “Degeneracy loci of families of Dirac operators”, Trans. Amer. Math. Soc., 364:11 (2012), 5995
V. Ya. Pidstrigach, “Hyperkähler Manifolds and Seiberg–Witten Equations”, Proc. Steklov Inst. Math., 246 (2004), 249–262
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
Kai Cieliebak, Ignasi Mundet i Riera, Dietmar A. Salamon, “Equivariant moduli problems, branched manifolds, and the Euler class”, Topology, 42:3 (2003), 641
N. A. Tyurin, “Instantons and monopoles”, Russian Math. Surveys, 57:2 (2002), 305–360
A. N. Tyurin, “Special Lagrangian geometry as slightly deformed algebraic geometry (geometric quantization and mirror symmetry)”, Izv. Math., 64:2 (2000), 363–437
B. V. Karpov, “$S$-duality testing and exceptional bundles”, Izv. Math., 63:1 (1999), 103–117
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
Paul M. N. Feehan, Thomas G. Leness, “$\rm PU(2)$ monopoles. I. Regularity, Uhlenbeck compactness, and transversality”, J. Differential Geom., 49:2 (1998)
B. V. Karpov, “On the algebraic geometry of $S$-duality”, Math. Notes, 61:2 (1997), 133–145
Christian Okonek, Andrei Teleman, “Quaternionic monopoles”, Comm Math Phys, 180:2 (1996), 363
N. A. Tyurin, “Necessary and sufficient conditions for a deformation of a B-monopole into an instanton”, Izv. Math., 60:1 (1996), 217–231
S. Donaldson, “The Seiberg-Witten equations and 4-manifold topology”, Bull. Amer. Math. Soc., 33:1 (1996), 45
Robert Friedman, Zhenbo Qin, “On complex surfaces diffeomorphic to rational surfaces”, Invent Math, 120:1 (1995), 81
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
A. N. Tyurin, “Canonical spin polynomials of an algebraic surface. I”, Russian Acad. Sci. Izv. Math., 45:3 (1995), 577–621
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
A. N. Tyurin, “Spin polynomial invariants of smooth structures on algebraic surfaces”, Russian Acad. Sci. Izv. Math., 42:2 (1994), 333–369
Zhenbo Qin, “On smooth structures of potential surfaces of general type homeomorphic to rational surfaces”, Invent Math, 113:1 (1993), 163
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