메뉴 건너뛰기




Volumn 206, Issue 1, 1999, Pages 105-136

Theta functions and Hodge numbers of moduli spaces of sheaves on rational surfaces

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0033239025     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050699     Document Type: Article
Times cited : (69)

References (46)
  • 2
    • 0002473270 scopus 로고
    • Sur la cohomologie de certaines espaces de modules de fibrés vectoriels
    • (Bombay, 1952) Bombay: Tata Inst. Fund. Res.
    • [Be] Beauville, A.: Sur la cohomologie de certaines espaces de modules de fibrés vectoriels. In: Geometry and Analysis. (Bombay, 1952) Bombay: Tata Inst. Fund. Res., 1995, pp. 37-40
    • (1995) Geometry and Analysis , pp. 37-40
    • Beauville, A.1
  • 3
    • 0032377338 scopus 로고    scopus 로고
    • Automorphic forms with singularities on Grassmannians
    • [Bo] Borcherds, R.: Automorphic forms with singularities on Grassmannians. Invent. Math. 132, 491-562 (1998)
    • (1998) Invent. Math. , vol.132 , pp. 491-562
    • Borcherds, R.1
  • 4
    • 0003270876 scopus 로고
    • Elliptic functions
    • Berlin Heidelberg: Springer-Verlag
    • [C] Chandrasekharan, K: Elliptic functions. Grundlehren 281, Berlin Heidelberg: Springer-Verlag, 1985
    • (1985) Grundlehren , vol.281
    • Chandrasekharan, K.1
  • 6
    • 0030551550 scopus 로고    scopus 로고
    • On the cohomology of Hilbert schemes of points
    • [Ch] Cheah, J.: On the cohomology of Hilbert schemes of points. J. Alg. Geom. 5, 479-511 (1996)
    • (1996) J. Alg. Geom. , vol.5 , pp. 479-511
    • Cheah, J.1
  • 7
    • 0001029146 scopus 로고
    • Newton Polyhedra and an algorithm for computing Hodge-Deligne numbers
    • [D-K] Danilov, V.I., Khovanskii, A.G.: Newton Polyhedra and an algorithm for computing Hodge-Deligne numbers. Math. USSR Izvestiya 29, 279-298 (1987)
    • (1987) Math. USSR Izvestiya , vol.29 , pp. 279-298
    • Danilov, V.I.1    Khovanskii, A.G.2
  • 8
    • 51649172369 scopus 로고
    • La conjecture de Weil I
    • [De] Deligne, P.: La conjecture de Weil I. Publ. Math. IHES 43, 273-307 (1974)
    • (1974) Publ. Math. IHES , vol.43 , pp. 273-307
    • Deligne, P.1
  • 9
    • 84941402488 scopus 로고
    • Variation of moduli spaces and Donaldson invariants under change of polarisation
    • [E-G] Ellingsrud, G. and Göttsche, L.: Variation of moduli spaces and Donaldson invariants under change of polarisation. J. reine angew. Math. 467, 1-49 (1995)
    • (1995) J. Reine Angew. Math. , vol.467 , pp. 1-49
    • Ellingsrud, G.1    Göttsche, L.2
  • 10
    • 0000302452 scopus 로고
    • On the homology of the Hilbert scheme of points in the plane
    • [E-S] Ellingsrud, G., Strømme, S.A.: On the homology of the Hilbert scheme of points in the plane. Invent. Math. 87, 343-352 (1987)
    • (1987) Invent. Math. , vol.87 , pp. 343-352
    • Ellingsrud, G.1    Strømme, S.A.2
  • 11
    • 0030556701 scopus 로고    scopus 로고
    • The blowup formula for Donaldson invariants
    • [F-S] Fintushel, R., Stern, R.: The blowup formula for Donaldson invariants. Ann. Math. 143, 529-546 (1996)
    • (1996) Ann. Math. , vol.143 , pp. 529-546
    • Fintushel, R.1    Stern, R.2
  • 12
    • 0000975014 scopus 로고
    • Algebraic families on an algebraic surface
    • [F] Fogarty, J.: Algebraic families on an algebraic surface. Am. J. Math. 90, 511-521 (1968)
    • (1968) Am. J. Math. , vol.90 , pp. 511-521
    • Fogarty, J.1
  • 17
    • 0002066831 scopus 로고
    • Flips of moduli spaces and transition formulas for Donaldson polynomial invariants of rational surfaces
    • [F-Q] Friedman, R., Qin, Z.: Flips of moduli spaces and transition formulas for Donaldson polynomial invariants of rational surfaces. Commun. in Analysis and Geometry 3, 11-83 (1995)
    • (1995) Commun. in Analysis and Geometry , vol.3 , pp. 11-83
    • Friedman, R.1    Qin, Z.2
  • 18
    • 0001341825 scopus 로고
    • The Betti numbers of the Hilbert schemes of points on a smooth projective surface
    • [Gö1] Göttsche, L.: The Betti numbers of the Hilbert schemes of points on a smooth projective surface. Math. Ann. 286, 193-207 (1990)
    • (1990) Math. Ann. , vol.286 , pp. 193-207
    • Göttsche, L.1
  • 19
    • 0000205236 scopus 로고    scopus 로고
    • Change of polarization and Hodge numbers of moduli spaces of torsion free sheaves on surfaces
    • [Gö2] Göttsche, L.: Change of polarization and Hodge numbers of moduli spaces of torsion free sheaves on surfaces. Math. Zeitschr. 223, 247-260 (1996)
    • (1996) Math. Zeitschr. , vol.223 , pp. 247-260
    • Göttsche, L.1
  • 21
    • 0030486634 scopus 로고    scopus 로고
    • Hodge numbers of moduli spaces of stable sheaves on K3 surfaces
    • [G-H] Göttsche, L., Huybrechts, D.: Hodge numbers of moduli spaces of stable sheaves on K3 surfaces. Int. J. Math. 7 No. 3, 359-372 (1996)
    • (1996) Int. J. Math. , vol.7 , Issue.3 , pp. 359-372
    • Göttsche, L.1    Huybrechts, D.2
  • 22
    • 0000372598 scopus 로고
    • Perverse sheaves and the cohomology of Hilbert schemes of smooth algebraic surfaces
    • [G-S] Göttsche, L., Soergel, W.: Perverse sheaves and the cohomology of Hilbert schemes of smooth algebraic surfaces. Math. Ann. 296, 235-245 (1993)
    • (1993) Math. Ann. , vol.296 , pp. 235-245
    • Göttsche, L.1    Soergel, W.2
  • 24
    • 0003346196 scopus 로고
    • Manifolds and modular forms
    • Braunschweig-Wiesbaden: Viehweg
    • [H-B-J] Hirzebruch, F., Berger, T., Jung, R.: Manifolds and modular forms. Aspects of Math. E20, Braunschweig-Wiesbaden: Viehweg, 1994
    • (1994) Aspects of Math. , vol.E20
    • Hirzebruch, F.1    Berger, T.2    Jung, R.3
  • 25
    • 0031087004 scopus 로고    scopus 로고
    • Birational symplectic manifolds and their deformations
    • [H] Huybrechts, D.: Birational symplectic manifolds and their deformations. J. Diff. Geom. 45, 488-513 (1997)
    • (1997) J. Diff. Geom. , vol.45 , pp. 488-513
    • Huybrechts, D.1
  • 26
    • 0003221353 scopus 로고    scopus 로고
    • The Geometry of Moduli Spaces of Sheaves
    • Braunschweig-Wiesbaden: Vieweg
    • [H-L] Huybrechts, D., Lehn, M.: The Geometry of Moduli Spaces of Sheaves. Aspects of Math. Vol. E 31, Braunschweig-Wiesbaden: Vieweg 1997
    • (1997) Aspects of Math. , vol.E 31
    • Huybrechts, D.1    Lehn, M.2
  • 27
    • 0010883610 scopus 로고
    • A generalized Jacobi theta function and quasimodular forms
    • R. Dijkgraaf, C. Faber, G. van der Geer (eds.) Boston: Birkhäuser
    • [K-Z] Kaneko, M., Zagier, D.: A generalized Jacobi theta function and quasimodular forms. In: R. Dijkgraaf, C. Faber, G. van der Geer (eds.) The moduli space of curves. Boston: Birkhäuser, 1995, pp. 165-172
    • (1995) The Moduli Space of Curves , pp. 165-172
    • Kaneko, M.1    Zagier, D.2
  • 29
    • 84972530014 scopus 로고
    • Embedded surfaces and the structure of Donaldson's Polynomial invariants
    • [Kr-M] Kronheimer, P., Mrowka, T.: Embedded surfaces and the structure of Donaldson's Polynomial invariants. J. Diff. Geom. 33, 573-734 (1995)
    • (1995) J. Diff. Geom. , vol.33 , pp. 573-734
    • Kronheimer, P.1    Mrowka, T.2
  • 30
    • 85037904311 scopus 로고    scopus 로고
    • Donaldson wall-crossing formulas via topology
    • to appear, dg-ga/960316
    • [L] Leness, T.G.: Donaldson wall-crossing formulas via topology. Forum Math. (1998) to appear, dg-ga/960316
    • (1998) Forum Math.
    • Leness, T.G.1
  • 34
    • 0009071881 scopus 로고    scopus 로고
    • Integration over the u-plane in Donaldson theory preprint hep-th/9709193
    • [M-W] Moore, G., Witten, E.: Integration over the u-plane in Donaldson theory preprint hep-th/9709193
    • Moore, G.1    Witten, E.2
  • 35
    • 0000748872 scopus 로고
    • Moduli of stable sheaves on ruled surfaces and their Picard groups
    • [Q1] Qin, Z.: Moduli of stable sheaves on ruled surfaces and their Picard groups. J. reine angew. Math. 433, 201-219 (1992)
    • (1992) J. Reine Angew. Math. , vol.433 , pp. 201-219
    • Qin, Z.1
  • 36
    • 84972511092 scopus 로고
    • Equivalence classes of polarizations and moduli spaces of sheaves
    • [Q2] Qin, Z.: Equivalence classes of polarizations and moduli spaces of sheaves. J. Diff. Geom. 37, 397-413 (1993)
    • (1993) J. Diff. Geom. , vol.37 , pp. 397-413
    • Qin, Z.1
  • 37
    • 0001859543 scopus 로고
    • A Strong Coupling Test of S-Duality
    • [V-W] Vafa, C., Witten, E.: A Strong Coupling Test of S-Duality. Nucl. Phys. B 431 (1994)
    • (1994) Nucl. Phys. B , vol.431
    • Vafa, C.1    Witten, E.2
  • 38
    • 0000368321 scopus 로고
    • Monopoles and four-manifolds
    • [W] Witten, E.: Monopoles and four-manifolds. Math. Research Letters 1, 769-796 (1994)
    • (1994) Math. Research Letters , vol.1 , pp. 769-796
    • Witten, E.1
  • 40
    • 0000814269 scopus 로고
    • The Betti numbers of the moduli space of stable sheaves of rank 2 on a ruled surface
    • [Y2] Yoshioka, K.: The Betti numbers of the moduli space of stable sheaves of rank 2 on a ruled surface. Math. Ann. 302, 519-540 (1995)
    • (1995) Math. Ann. , vol.302 , pp. 519-540
    • Yoshioka, K.1
  • 41
    • 0030507479 scopus 로고    scopus 로고
    • Chamber structure of polarizations and the moduli space of stable sheaves on a ruled surface
    • [Y3] Yoshioka, K.: Chamber structure of polarizations and the moduli space of stable sheaves on a ruled surface. Int. J. Math. 7, 411-431 (1996)
    • (1996) Int. J. Math. , vol.7 , pp. 411-431
    • Yoshioka, K.1
  • 43
    • 16144367495 scopus 로고    scopus 로고
    • Betti numbers of moduli of stable sheaves on some surfaces
    • [Y5] Yoshioka, K., Betti numbers of moduli of stable sheaves on some surfaces. Nucl. Phys. B (Proc. Suppl.) 46, 263-268 (1996)
    • (1996) Nucl. Phys. B , vol.46 , Issue.PROC. SUPPL. , pp. 263-268
    • Yoshioka, K.1
  • 44
    • 0003181059 scopus 로고    scopus 로고
    • q-rational points of moduli of stable sheaves on elliptic surfaces. Moduli of vector bundles
    • Marcel Dekker
    • q-rational points of moduli of stable sheaves on elliptic surfaces. Moduli of vector bundles, Lect. Notes in Pure and Applied Math. 179, Marcel Dekker, 297-305
    • Lect. Notes in Pure and Applied Math. , vol.179 , pp. 297-305
    • Yoshioka, K.1
  • 45
    • 0000237910 scopus 로고
    • Periods of modular forms and Jacobi theta functions
    • [Z1] Zagier, D.: Periods of modular forms and Jacobi theta functions. Invent. math. 104, 449-465 (1991)
    • (1991) Invent. Math. , vol.104 , pp. 449-465
    • Zagier, D.1
  • 46
    • 0002556812 scopus 로고
    • Introduction to Modular forms
    • eds. W. Waldschmidt, P. Moussa, J.-M. Luck, C. Itzykson, Berlin-Heidelberg: Springer-Verlag
    • [Z2] Zagier, D.: Introduction to Modular forms. In: From Number Theory to Physics, eds. W. Waldschmidt, P. Moussa, J.-M. Luck, C. Itzykson, Berlin-Heidelberg: Springer-Verlag, 1992
    • (1992) From Number Theory to Physics
    • Zagier, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.