Hodge theory and deformations of maps

Ziv Ran

Compositio Mathematica (1995)

  • Volume: 97, Issue: 3, page 309-328
  • ISSN: 0010-437X

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Ran, Ziv. "Hodge theory and deformations of maps." Compositio Mathematica 97.3 (1995): 309-328. <http://eudml.org/doc/90386>.

@article{Ran1995,
author = {Ran, Ziv},
journal = {Compositio Mathematica},
keywords = {base change; formal schemes; Hodge-type group; unobstructed deformations},
language = {eng},
number = {3},
pages = {309-328},
publisher = {Kluwer Academic Publishers},
title = {Hodge theory and deformations of maps},
url = {http://eudml.org/doc/90386},
volume = {97},
year = {1995},
}

TY - JOUR
AU - Ran, Ziv
TI - Hodge theory and deformations of maps
JO - Compositio Mathematica
PY - 1995
PB - Kluwer Academic Publishers
VL - 97
IS - 3
SP - 309
EP - 328
LA - eng
KW - base change; formal schemes; Hodge-type group; unobstructed deformations
UR - http://eudml.org/doc/90386
ER -

References

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  1. [B] Bloch, S.Semi-regularity and de Rham cohomology, Invent. math.17 (1972), 51-66. Zbl0254.14011MR325613
  2. [D] Deligne, P.Théorème de Lefschetz et critères de dégénérescence de suits spectrales, Publ. Math. IHES, 35 (1968), 197-226. Zbl0159.22501MR244265
  3. [F] Fujiki, A.On automorphism groups of compact Kähler manifolds, Invent. Math.44 (1978), 225-258. Zbl0367.32004MR481142
  4. [L] Lichnérowicz, A.Sur les transformations analytiques des variétés Kähleriennes. C.R. Acad. Sci. Paris244 (1957), 3011-3014. Zbl0080.37501MR94479
  5. [NS] Narasimhan, M.S., Seshadri, C.S.Stable and unitary vector bundles on a compact Riemann surface. Ann. of Math.82 (1965), 540-567. Zbl0171.04803MR184252
  6. [R1] Ran, Z.Deformations of manifolds with torsion or negative canonical bundle. J. Algebraic Geometry, 1 (1992), 279-292. Zbl0818.14003MR1144440
  7. [R2] Ran, Z.Lifting of cohomology and deformations of certain holomorphic maps. Bull. AMS26 (1992), 113-117. Zbl0749.32010MR1102754
  8. [R3] Ran, Z.Hodge theory and the Hilbert scheme. J. Differential Geometry37 (1993), 191-198; Erratum & Addendum (to appear). Zbl0804.14004MR1198605
  9. [R4] Ran, Z.The structure of Gauss-like maps. Compositio Math.32 (1984), 171-177 Zbl0547.14004MR750353
  10. [R5] Ran, Z.Deformations of maps. In: Algebraic curves and projective geometry, E. Ballico, C. Cilberto, eds., Lecture notes in Math1389. Berlin: Springer1989. Zbl0708.14006MR1023402
  11. [R6] Ran, Z.Deformations of Calabi-Yau Kleinfolds. In: Essays on mirror manifolds, S. T. Yau ed. pp. 451-457. Hong Kong: International Press1992. Zbl0827.32021MR1191436
  12. [R7] Ran, Z.Canonical infinitesimal deformations. Preprint. Zbl1060.14016MR1713519
  13. [S] Schlessinger, M.Functors of Artin rings, Trans. AMS130 (1968), 208-222. Zbl0167.49503MR217093
  14. [U] Ueno, K.Classification theory of algebraic varieties and compact complex spaces. Lecture notes in Math. 439. Berlin: Springer1975. Zbl0299.14007MR506253
  15. [V] Voisin, C.Sur la stabilité des sous-variétés lagrangiennes des variétés symplectiques holomorphes. Preprint. Zbl0765.32012MR1201391
  16. [Z] Zariski, O.Theorem of Riemann-Roch for high multiples of an effective divisor on an algebraic surface. Ann. Math.76 (1962), 560-615. Zbl0124.37001MR141668

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