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Volumn 58, Issue 2, 2001, Pages 331-370

Uniqueness of symplectic canonical class, surface cone and symplectic cone of 4-manifolds with B+ = 1

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EID: 0035384517     PISSN: 0022040X     EISSN: 1945743X     Source Type: Journal    
DOI: 10.4310/jdg/1090348329     Document Type: Article
Times cited : (95)

References (54)
  • 1
    • 0031285533 scopus 로고    scopus 로고
    • Symplectic packings in dimension 4
    • P. Biran, Symplectic packings in dimension 4, Geom. and Funct. Anal. 7(3) (1997) 420-437.
    • (1997) Geom. and Funct. Anal , vol.7 , Issue.3 , pp. 420-437
    • Biran, P.1
  • 4
    • 0001294652 scopus 로고    scopus 로고
    • The canonical class and the C, cx properties of Kdhler surfaces
    • cx properties of Kdhler surfaces, New York J. Math. 2 (1996), 103-146.
    • (1996) New York J. Math , vol.2 , pp. 103-146
    • Brussee, R.1
  • 6
    • 0030293308 scopus 로고    scopus 로고
    • Symplectic submanifolds and almost-complex geometry
    • S. Donaldson, Symplectic submanifolds and almost-complex geometry, J. Differen-tial Geom. 44(4) (1996) 666-705.
    • (1996) J. Differen-Tial Geom , vol.44 , Issue.4 , pp. 666-705
    • Donaldson, S.1
  • 8
    • 0000197201 scopus 로고
    • Immersed spheres in 4-manifolds and the immersed Thom conjecture
    • R. Fintushel & R. Stern, Immersed spheres in 4-manifolds and the immersed Thom conjecture, Turkish J. Math. 19 (1995), 145-157.
    • (1995) Turkish J. Math , vol.19 , pp. 145-157
    • Fintushel, R.1    Stern, R.2
  • 9
    • 0032353343 scopus 로고    scopus 로고
    • Knots, links, and 4-manifolds
    • R. Fintushel & R. Stern, Knots, links, and 4-manifolds, Invent. Math. 134(2) (1998) 363-400.
    • (1998) Invent. Math. , vol.134 , Issue.2 , pp. 363-400
    • Fintushel, R.1    Stern, R.2
  • 10
    • 84972526312 scopus 로고
    • On the diffeomorphism types of certain algebraic sur-faces
    • R. Friedman & J. Morgan, On the diffeomorphism types of certain algebraic sur-faces, J. Differential Geom. 27(3) (1988) 371-398.
    • (1988) J. Differential Geom , vol.27 , Issue.3 , pp. 371-398
    • Friedman, R.1    Morgan, J.2
  • 11
    • 0040484628 scopus 로고    scopus 로고
    • Algebraic surfaces and Seiberg-Witten invariants
    • R. Friedman & J. Morgan, Algebraic surfaces and Seiberg-Witten invariants, J. Algebraic Geom. 6(3) (1997) 445-479.
    • (1997) J. Algebraic Geom , vol.6 , Issue.3 , pp. 445-479
    • Friedman, R.1    Morgan, J.2
  • 12
    • 84973999231 scopus 로고
    • Symplectic structures on T2-bundles over T
    • 2, Duke Math. Journal, 67(3) (1992) 539-555.
    • (1992) Duke Math. Journal , vol.67 , Issue.3 , pp. 539-555
    • Geiges, H.1
  • 13
    • 0040804374 scopus 로고
    • Pseudo-holomorphic curves in symplectic manifolds
    • M. Gromov, Pseudo-holomorphic curves in symplectic manifolds, Invent. Math. 82 (1985) 307-347.
    • (1985) Invent. Math , vol.82 , pp. 307-347
    • Gromov, M.1
  • 14
    • 0031287699 scopus 로고    scopus 로고
    • The Gromov invariants of Ruan-Tian and Taubes
    • E.-N. Ionel & T. Parker, The Gromov invariants of Ruan-Tian and Taubes, Math. Res. Letter 4 (1997), 521-532.
    • (1997) Math. Res. Letter , vol.4 , pp. 521-532
    • Ionel, E.-N.1    Parker, T.2
  • 16
    • 0032608083 scopus 로고    scopus 로고
    • Minimal genus in S1 x M3
    • 3, Invent. Math. 135(1) (1999) 45-61.
    • (1999) Invent. Math , vol.135 , Issue.1 , pp. 45-61
    • Kronheimer, P.1
  • 17
    • 0000317662 scopus 로고
    • Isotopy of symplectic balls, Gromov’s radius and the structure of ruled symplectic 4-manifolds
    • F. Lalonde, Isotopy of symplectic balls, Gromov’s radius and the structure of ruled symplectic 4-manifolds, Math. Ann. 300 (1994) 273-296.
    • (1994) Math. Ann , vol.300 , pp. 273-296
    • Lalonde, F.1
  • 18
    • 0030300394 scopus 로고    scopus 로고
    • The classification of ruled symplectic 4-manifolds
    • F. Lalonde & D. McDuff, The classification of ruled symplectic 4-manifolds, Math. Res. Lett. 3(6) (1996) 769-778.
    • (1996) Math. Res. Lett , vol.3 , Issue.6 , pp. 769-778
    • Lalonde, F.1    McDuff, D.2
  • 19
    • 0012669308 scopus 로고    scopus 로고
    • Diffeomorphisms, symplectic forms, and Kodaira fibrations
    • C. LeBrun, Diffeomorphisms, symplectic forms, and Kodaira fibrations, Geom. Topol. 4 (2000), 451-456.
    • (2000) Geom. Topol , vol.4 , pp. 451-456
    • Lebrun, C.1
  • 21
    • 0037498687 scopus 로고    scopus 로고
    • Symplectic genus, minimal genus and, diffeomorphisms
    • to appear
    • B.H. Li & T.J. Li, Symplectic genus, minimal genus and, diffeomorphisms, to appear in Asian J. Math.
    • Asian J. Math
    • Li, B.H.1    Li, T.J.2
  • 22
    • 22444453854 scopus 로고    scopus 로고
    • Smoothly embedded spheres in symplectic four manifolds
    • T.J. Li, Smoothly embedded spheres in symplectic four manifolds, Proc. Amer. Math. Soc. 127(2) (1999) 609-613.
    • (1999) Proc. Amer. Math. Soc , vol.127 , Issue.2 , pp. 609-613
    • Li, T.J.1
  • 23
    • 0001027289 scopus 로고    scopus 로고
    • Symplectic Parshin-Arakelov inequality
    • T.J. Li, Symplectic Parshin-Arakelov inequality, Internat. Math. Res. Notices 2000, 18 941-954.
    • (2000) Internat. Math. Res. Notices , vol.18 , pp. 941-954
    • Li, T.J.1
  • 24
    • 21844520385 scopus 로고
    • General wall crossing formula
    • T.J. Li & A. Liu, General wall crossing formula, Math. Res. Letter 2 (1995) 797-810.
    • (1995) Math. Res. Letter , vol.2 , pp. 797-810
    • Li, T.J.1    Liu, A.2
  • 25
    • 0001670686 scopus 로고
    • Symplectic structures on ruled surfaces and a generalized ad-junction inequality
    • T.J. Li & A. Liu, Symplectic structures on ruled surfaces and a generalized ad-junction inequality, Math. Res. Letters 2 (1995) 453-471.
    • (1995) Math. Res. Letters , vol.2 , pp. 453-471
    • Li, T.J.1    Liu, A.2
  • 26
    • 0012671929 scopus 로고    scopus 로고
    • Family Seiberg-Witten invariants and wall crossing formulas
    • T.J. Li & A. Liu, Family Seiberg-Witten invariants and wall crossing formulas, Comm. Anal. Geom. 9 (2001) 777-823.
    • (2001) Comm. Anal. Geom. , vol.9 , pp. 777-823
    • Li, T.J.1    Liu, A.2
  • 27
    • 0345759529 scopus 로고    scopus 로고
    • On the equivalence between SW and GT in the case b+ = 1
    • T.J. Li & A. Liu, On the equivalence between SW and GT in the case b+ = 1, Internat. Math. Res. Notices 1999 7 335-345.
    • (1999) Internat. Math. Res. Notices , vol.7 , pp. 335-345
    • Li, T.J.1    Liu, A.2
  • 28
    • 0030300558 scopus 로고    scopus 로고
    • Some new applications of the general wall crossing formula
    • A. Liu, Some new applications of the general wall crossing formula, Math. Res. Letters 3 (1996) 569-585.
    • (1996) Math. Res. Letters , vol.3 , pp. 569-585
    • Liu, A.1
  • 29
    • 84968502808 scopus 로고
    • The structure of rational and, ruled symplectic 4-manifolds
    • D. McDuff, The structure of rational and, ruled symplectic 4-manifolds J. Amer. Math. Soc. 3(3) (1990) 679-712.
    • (1990) J. Amer. Math. Soc , vol.3 , Issue.3 , pp. 679-712
    • McDuff, D.1
  • 30
    • 0002825874 scopus 로고    scopus 로고
    • With notes by Wladyslav Lorek, Gauge theory and symplectic geometry (Montreal, PQ, 1995), Kluwer Acad. Publ., Dordrecht
    • D. McDuff, Lectures on Gromov invariants for symplectic 4-manifolds, With notes by Wladyslav Lorek, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 488, Gauge theory and symplectic geometry (Montreal, PQ, 1995) 175-210, Kluwer Acad. Publ., Dordrecht, 1997.
    • (1997) Lectures on Gromov Invariants for Symplectic 4-Manifolds , vol.488 , pp. 175-210
    • McDuff, D.1
  • 31
    • 0012711111 scopus 로고    scopus 로고
    • From symplectic deformation to isotopy
    • (Irvine, CA, 1996), Press, Cambridge, MA
    • D. McDuff, From symplectic deformation to isotopy (Irvine, CA, 1996), 85-99, First Int. Press Lect Ser. I, Internat. Press, Cambridge, MA, 1998.
    • (1998) First Int. Press Lect Ser. I, Internat , pp. 85-99
    • McDuff, D.1
  • 32
    • 0001753153 scopus 로고
    • Immersed spheres in symplectic 4-manifolds
    • D. McDuff, Immersed spheres in symplectic 4-manifolds, Ann. Inst. Fourier (Grenoble) 42(bf 1-2) (1992) 369-392.
    • (1992) Ann. Inst. Fourier (Grenoble) , vol.42 , pp. 369-392
    • McDuff, D.1
  • 33
    • 0000625572 scopus 로고
    • Blow ups and symplectic embeddings in dimension 4
    • D. McDuff, Blow ups and symplectic embeddings in dimension 4, Topology 30 (1991) 409-421.
    • (1991) Topology , vol.30 , pp. 409-421
    • McDuff, D.1
  • 34
    • 0001082464 scopus 로고
    • Symplectic packings and algebraic geometry
    • D. McDuff & L. Polterovich, Symplectic packings and algebraic geometry, Invent. Math. 115(3) (1994) 405-434.
    • (1994) Invent. Math. , vol.115 , Issue.3 , pp. 405-434
    • McDuff, D.1    Polterovich, L.2
  • 35
    • 0002319198 scopus 로고    scopus 로고
    • A survey of symplectic 4-manifolds with b+ = 1
    • D. McDuff & D. Salamon, A survey of symplectic 4-manifolds with b+ = 1, Turkish J. Math. 20(1) (1996) 47-60.
    • (1996) Turkish J. Math , vol.20 , Issue.1 , pp. 47-60
    • McDuff, D.1    Salamon, D.2
  • 36
    • 0033235851 scopus 로고    scopus 로고
    • 4-manifolds with inequivalent symplectic forms and, 3-manifolds with inequivalent fibrations
    • C. McMullen & C. Taubes, 4-manifolds with inequivalent symplectic forms and, 3-manifolds with inequivalent fibrations, Math. Res. Lett. 6(5-6) (1999) 681-696.
    • (1999) Math. Res. Lett , vol.6 , Issue.5-6 , pp. 681-696
    • McMullen, C.1    Taubes, C.2
  • 37
    • 0035584891 scopus 로고    scopus 로고
    • On the moduli space of diffeomorphic algebraic surfaces
    • to appear
    • M. Manetti, On the moduli space of diffeomorphic algebraic surfaces, Inv. Math. (2001) to appear.
    • (2001) Inv. Math
    • Manetti, M.1
  • 39
    • 84968494100 scopus 로고
    • On the volume elements on a manifold
    • J. Moser, On the volume elements on a manifold, Trans. Amer. Math. Soc. 120 (1965) 286-294.
    • (1965) Trans. Amer. Math. Soc , vol.120 , pp. 286-294
    • Moser, J.1
  • 40
    • 0040645397 scopus 로고    scopus 로고
    • Notes on symplectic 4-manifolds with b+ = 1, II
    • H. Ohta & K. Ono, Notes on symplectic 4-manifolds with b+ = 1, II, Internat. J. Math. 7(6) (1996) 755-770.
    • (1996) Internat. J. Math , vol.7 , Issue.6 , pp. 755-770
    • Ohta, H.1    Ono, K.2
  • 41
    • 0030359827 scopus 로고    scopus 로고
    • Seiberg-Witten invariants for manifolds with b+ = 1 and the universal wall crossing formula
    • C. Okonek & A. Teleman, Seiberg-Witten invariants for manifolds with b+ = 1 and the universal wall crossing formula, Internat. J. Math. 7(6) (1996) 811-832.
    • (1996) Internat. J. Math , vol.7 , Issue.6 , pp. 811-832
    • Okonek, C.1    Teleman, A.2
  • 42
    • 84972496549 scopus 로고
    • Symplectic topology on algebraic 3-folds
    • Y.B. Ruan, Symplectic topology on algebraic 3-folds, J. Differential Geom. 39(1) (1994) 215-227.
    • (1994) J. Differential Geom , vol.39 , Issue.1 , pp. 215-227
    • Ruan, Y.B.1
  • 43
    • 0000358761 scopus 로고
    • Symplectic topology and extremal rays
    • Y.B. Ruan, Symplectic topology and extremal rays, Geom. Funct. Anal. 3(4) (1993) 395-430.
    • (1993) Geom. Funct. Anal , vol.3 , Issue.4 , pp. 395-430
    • Ruan, Y.B.1
  • 44
    • 0003049935 scopus 로고
    • Symplectic topology and complex surfaces
    • World Sci. Publishing, River Edge, NJ
    • Y.B. Ruan, Symplectic topology and complex surfaces, Geometry and analysis on complex manifolds, 171-197, World Sci. Publishing, River Edge, NJ, 1994.
    • (1994) Geometry and Analysis on Complex Manifolds , pp. 171-197
    • Ruan, Y.B.1
  • 45
    • 0029682448 scopus 로고
    • A mathematical theory of quantum cohomology
    • Y.B. Ruan & G. Tian, A mathematical theory of quantum cohomology, J. Differ-ential Geom. 42(2) (1995) 259-367.
    • (1995) J. Differ-Ential Geom , vol.42 , Issue.2 , pp. 259-367
    • Ruan, Y.B.1    Tian, G.2
  • 47
    • 0034348697 scopus 로고    scopus 로고
    • On moduli spaces of symplectic forms
    • I. Smith, On moduli spaces of symplectic forms, Math. Res. Lett. 7(5-6) (2000) 779-788.
    • (2000) Math. Res. Lett , vol.7 , Issue.5-6 , pp. 779-788
    • Smith, I.1
  • 48
    • 0000368324 scopus 로고
    • The Seiberg-Witten invariants and symplectic forms
    • C.H. Taubes, The Seiberg-Witten invariants and symplectic forms, Math. Re-search Letters 1 (1994) 809-822.
    • (1994) Math. Re-Search Letters , vol.1 , pp. 809-822
    • Taubes, C.H.1
  • 49
    • 0002225840 scopus 로고
    • More constraints on symplectic manifolds from Seiberg-Witten in-variants
    • C.H. Taubes, More constraints on symplectic manifolds from Seiberg-Witten in-variants, Math. Research Letters, 2 (1995) 9-14.
    • (1995) Math. Research Letters , vol.2 , pp. 9-14
    • Taubes, C.H.1
  • 50
    • 0000973618 scopus 로고
    • The Seiberg-Witten invariants and the Gromov invariants
    • C.H. Taubes, The Seiberg-Witten invariants and the Gromov invariants, Math. Research Letters 2 (1995) 221-238.
    • (1995) Math. Research Letters , vol.2 , pp. 221-238
    • Taubes, C.H.1
  • 51
    • 0030292537 scopus 로고    scopus 로고
    • Counting pseudo-holomorphic submanifolds in dimension 4
    • C.H. Taubes, Counting pseudo-holomorphic submanifolds in dimension 4, J. Dif-ferential Geom. 44 (1996) 818-893.
    • (1996) J. Dif-Ferential Geom , vol.44 , pp. 818-893
    • Taubes, C.H.1
  • 52
    • 84966204143 scopus 로고
    • Some simple examples of symplectic manifolds
    • W. Thurston, Some simple examples of symplectic manifolds, Proc. Amer. Math. Soc. 55 (1976) 467-468.
    • (1976) Proc. Amer. Math. Soc , vol.55 , pp. 467-468
    • Thurston, W.1
  • 53
    • 0000360091 scopus 로고    scopus 로고
    • Homotopy K3’s with several symplectic structures
    • S. Vidussi, Homotopy K3’s with several symplectic structures, Geom. Topol. 5 (2001) 267-285
    • (2001) Geom. Topol , vol.5 , pp. 267-285
    • Vidussi, S.1
  • 54
    • 0000368321 scopus 로고
    • Monoples and Four-manifolds
    • E. Witten, Monoples and Four-manifolds, Math. Res. Letters 1 (1994) 769-79.
    • (1994) Math. Res. Letters , vol.1 , pp. 769-779
    • Witten, E.1


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