Some applications of the theory of harmonic integrals

• Autorzy: Shin-ichi Matsumura
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Injectivity theorems; Singular metrics; Multiplier ideal sheaves; The theory of harmonic integrals; L2-methods

Kategorie tematyczne

• 32L10: Sheaves and cohomology of sections of holomorphic vector bundles, general results
• 32L20: Vanishing theorems
• 14F18: Multiplier ideals

• Wydawca: De Gruyter Open
• Czasopismo: Complex Manifolds
• Rocznik: 2015
• Tom: 2
• Numer: 1

Daty

otrzymano

2014-11-25

zaakceptowano

2015-06-03

online

2015-07-08

Twórcy

autor

Shin-ichi Matsumura

• Mathematical Institute, Tohoku University, 6-3, Aramaki Aza-Aoba, Aoba-ku,
  Sendai 980-8578, Japan

Bibliografia

• [1] J.-P. Demailly. Analytic methods in algebraic geometry. Surveys of Modern Mathematics 1, International Press, Somerville, Higher Education Press, Beijing, (2012).
• [2] J.-P. Demailly. Complex analytic and differential geometry. Lecture Notes on the web page of the author.
• [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.
• [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]
• [5] I. Enoki. Kawamata-Viehweg vanishing theorem for compact Kähler manifolds. Einstein metrics and Yang-Mills connections (Sanda, 1990), 59–68.
• [6] H. Esnault, E. Viehweg. Lectures on vanishing theorems. DMV Seminar, 20. Birkhäuser Verlag, Basel, (1992).
• [7] O. Fujino. A transcendental approach to Kollár’s injectivity theorem. Osaka J. Math. 49 (2012), no. 3, 833–852.
• [8] O. Fujino. A transcendental approach to Kollár’s injectivity theorem II. J. Reine Angew. Math. 681 (2013), 149–174.
• [9] Y. Gongyo, S. Matsumura. Versions of injectivity and extension theorems. Preprint, arXiv:1406.6132v2.
• [10] J. Kollár. Higher direct images of dualizing sheaves. I. Ann. of Math. (2) 123 (1986), no. 1, 11–42.
• [11] S. Matsumura. An injectivity theorem with multiplier ideal sheaves of singular metrics with transcendental singularities. Preprint, arXiv:1308.2033v2.
• [12] S. Matsumura. A Nadel vanishing theorem via injectivity theorems. Math. Ann. 359 (2014) no.4, 785–802. [WoS]
• [13] S. Matsumura. A Nadel vanishing theorem for metrics with minimal singularities on big line bundles. Adv. in Math. 359 (2015), 188–207 [WoS]
• [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.
• [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.
• [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]

Identyfikatory

DOI

10.1515/coma-2015-0003