Some applications of the theory of harmonic integrals

Shin-ichi Matsumura

Complex Manifolds (2015)

  • Volume: 2, Issue: 1, page 16-25, electronic only
  • ISSN: 2300-7443

Abstract

top
In this survey, we present recent techniques on the theory of harmonic integrals to study the cohomology groups of the adjoint bundle with the multiplier ideal sheaf of singular metrics. As an application, we give an analytic version of the injectivity theorem.

How to cite

top

Shin-ichi Matsumura. "Some applications of the theory of harmonic integrals." Complex Manifolds 2.1 (2015): 16-25, electronic only. <http://eudml.org/doc/275941>.

@article{Shin2015,
abstract = {In this survey, we present recent techniques on the theory of harmonic integrals to study the cohomology groups of the adjoint bundle with the multiplier ideal sheaf of singular metrics. As an application, we give an analytic version of the injectivity theorem.},
author = {Shin-ichi Matsumura},
journal = {Complex Manifolds},
keywords = {Injectivity theorems; Singular metrics; Multiplier ideal sheaves; The theory of harmonic integrals; L2-methods; injectivity theorems; singular metrics; multiplier ideal sheaves; theory of harmonic integrals; -methods},
language = {eng},
number = {1},
pages = {16-25, electronic only},
title = {Some applications of the theory of harmonic integrals},
url = {http://eudml.org/doc/275941},
volume = {2},
year = {2015},
}

TY - JOUR
AU - Shin-ichi Matsumura
TI - Some applications of the theory of harmonic integrals
JO - Complex Manifolds
PY - 2015
VL - 2
IS - 1
SP - 16
EP - 25, electronic only
AB - In this survey, we present recent techniques on the theory of harmonic integrals to study the cohomology groups of the adjoint bundle with the multiplier ideal sheaf of singular metrics. As an application, we give an analytic version of the injectivity theorem.
LA - eng
KW - Injectivity theorems; Singular metrics; Multiplier ideal sheaves; The theory of harmonic integrals; L2-methods; injectivity theorems; singular metrics; multiplier ideal sheaves; theory of harmonic integrals; -methods
UR - http://eudml.org/doc/275941
ER -

References

top
  1. [1] J.-P. Demailly. Analytic methods in algebraic geometry. Surveys of Modern Mathematics 1, International Press, Somerville, Higher Education Press, Beijing, (2012). 
  2. [2] J.-P. Demailly. Complex analytic and differential geometry. Lecture Notes on the web page of the author. 
  3. [3] J.-P. Demailly. Estimations L2 pour l’opérateur @ d’un fibré vectoriel holomorphe semi-positif au-dessus d’une variété kählérienne complète. Ann. Sci. École Norm. Sup(4). 15 (1982), no. 3, 457–511. Zbl0507.32021
  4. [4] J.-P. Demailly, T. Peternell, M. Schneider. Pseudo-effective line bundles on compact Kähler manifolds. Internat. J. Math. 12 (2001), no. 6, 689–741. [Crossref] Zbl1111.32302
  5. [5] I. Enoki. Kawamata-Viehweg vanishing theorem for compact Kähler manifolds. Einstein metrics and Yang-Mills connections (Sanda, 1990), 59–68. Zbl0797.53052
  6. [6] H. Esnault, E. Viehweg. Lectures on vanishing theorems. DMV Seminar, 20. Birkhäuser Verlag, Basel, (1992). Zbl0779.14003
  7. [7] O. Fujino. A transcendental approach to Kollár’s injectivity theorem. Osaka J. Math. 49 (2012), no. 3, 833–852. Zbl1270.32004
  8. [8] O. Fujino. A transcendental approach to Kollár’s injectivity theorem II. J. Reine Angew. Math. 681 (2013), 149–174. Zbl1285.32009
  9. [9] Y. Gongyo, S. Matsumura. Versions of injectivity and extension theorems. Preprint, arXiv:1406.6132v2. 
  10. [10] J. Kollár. Higher direct images of dualizing sheaves. I. Ann. of Math. (2) 123 (1986), no. 1, 11–42. Zbl0598.14015
  11. [11] S. Matsumura. An injectivity theorem with multiplier ideal sheaves of singular metrics with transcendental singularities. Preprint, arXiv:1308.2033v2. 
  12. [12] S. Matsumura. A Nadel vanishing theorem via injectivity theorems. Math. Ann. 359 (2014) no.4, 785–802. [WoS] Zbl1327.14092
  13. [13] S. Matsumura. A Nadel vanishing theorem for metrics with minimal singularities on big line bundles. Adv. in Math. 359 (2015), 188–207 [WoS] Zbl06441135
  14. [14] T. Ohsawa. On a curvature condition that implies a cohomology injectivity theorem of Kollár-Skoda type. Publ. Res. Inst. Math. Sci. 41 (2005), no. 3, 565–577. Zbl1103.32005
  15. [15] K. Takegoshi. On cohomology groups of nef line bundles tensorized with multiplier ideal sheaves on compact Kähler manifolds. Osaka J. Math. 34 (1997), no. 4, 783–802. Zbl0895.32008
  16. [16] S. G. Tankeev. On n-dimensional canonically polarized varieties and varieties of fundamental type.Math. USSR-Izv. 5 (1971), no. 1, 29–43.[Crossref] Zbl0248.14005

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.