Singular Hermitian Metrics / Analytic Theory of Moduli Spaces

• Applicant: Professor Dr. Georg Schumacher
• Subject Area: Mathematics
• Term: from 2007 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 48226760

• Final Report Year: 2023

Final Report Abstract

No abstract available

Publications

• Multiplier Ideal Sheaves in Algebraic and Complex Geometry. Oberwolfach Reports, 6(2), 1101-1156.
  Kebekus, Stefan; Păun, Mihai; Schumacher, Georg & Siu, Yum-Tong
  
• Curvature of higher direct images and applications, 30 p., arXiv: 1002.4858
  Schumacher, Georg
  
• Geometric approach to the Weil–Petersson symplectic form. Commentarii Mathematici Helvetici, 85(2), 243-257.
  Axelsson, Reynir & Schumacher, Georg
  
• Vector bundles on Sasakian manifolds. Advances in Theoretical and Mathematical Physics, 14(2), 541-562.
  Biswas, Indranil & Schumacher, Georg
  
• Deligne pairing and determinant bundle. Electronic Research Announcements in Mathematical Sciences, 18(0), 91-96.
  Weng, Lin; Schumacher, Georg & Biswas, Indranil
  
• Weil-Petersson geometry for families of hyperbolic conical Riemann surfaces. Michigan Mathematical Journal, 60(1).
  Schumacher, Georg & Trapani, Stefano
  
• In Memoriam Horst Tietz (1921–2012). Jahresbericht der Deutschen Mathematiker-Vereinigung, 114(4), 209-213.
  Schumacher, Georg
  
• Positivity of relative canonical bundles and applications. Inventiones mathematicae, 190(1), 1-56.
  Schumacher, Georg
  
• Variation of geodesic length functions in families of Kähler-Einstein manifolds and applications to Teichmüller space. Annales Academiae Scientiarum Fennicae Mathematica, 37(2012, 2), 91-106.
  Axelsson, Reynir & Schumacher, Georg
  
• Funktionentheorie 1. 5., neu bearb. Aufl. Berlin: Springer. xx, 402 p. (2013)
  Remmert, Reinhold & Schumacher, Georg
  
• Funktionentheorie. 2., 3rd new revised ed. Springer-Lehrbuch. Berlin: Springer. xvii, 383 p. (2013)
  Remmert, Reinhold & Schumacher, Georg
  
• Curvature properties for moduli of canonically polarized manifolds—An analogy to moduli of Calabi–Yau manifolds. Comptes Rendus. Mathématique, 352(10), 835-840.
  Schumacher, Georg
  
• Deligne pairing and Quillen metric. International Journal of Mathematics, 25(14), 1450122.
  Biswas, Indranil & Schumacher, Georg
  
• Kähler structure on Hurwitz spaces. Manuscripta Mathematica, 147(1-2), 63-79.
  Axelsson, Reynir; Biswas, Indranil & Schumacher, Georg
  
• A criterion for a degree-one holomorphic map to be a biholomorphism. Complex Variables and Elliptic Equations, 62(7), 914-918.
  Bharali, Gautam; Biswas, Indranil & Schumacher, Georg
  
• The Weil-Petersson current for moduli of vector bundles and applications to orbifolds. Annales de la Faculté des sciences de Toulouse : Mathématiques, 25(4), 895-917.
  Biswas, Indranil & Schumacher, Georg
  
• An Extension Theorem for Hermitian Line Bundles. Analytic and Algebraic Geometry (2017), 225-237. Springer Singapore.
  Schumacher, Georg
  
• Curvature of higher direct image sheaves. Advanced Studies in Pure Mathematics (NA), 171-184. Mathematical Society of Japan.
  Geiger, Thomas & Schumacher, Georg
  
• Differential geometry of moduli spaces of quiver bundles. Journal of Geometry and Physics, 118(2017, 8), 51-66.
  Biswas, Indranil & Schumacher, Georg
  
• Line bundles and flat connections. Proceedings - Mathematical Sciences, 127(3), 547-549.
  BISWAS, INDRANIL & SCHUMACHER, GEORG
  
• Application of Cheeger-Gromov theory to the 12-cohomology of harmoiiic Higgs bundles over covcring of finite voliime c.omplete manifolds. arXiv:1810.03863
  Schumacher, Georg & Dingoyan, Pascal
  
• Moduli of canonically polarized manifolds, higher order Kodaira-Spencer maps, and an analogy to Calabi-Yau manifolds, in: Uniformization, Riemann-Hilbert Correspondence, Calabi-Yau Manifolds, and Picard-Fuchs Equations. ALM 42 (2018), pp. 371-401; arXiv: 1702.07628
  Schumacher, Georg
  
• Symplectic reduction of Sasakian manifolds. Proceedings - Mathematical Sciences, 129(4).
  Biswas, Indranil & Schumacher, Georg
  
• Branched holomorphic Cartan geometry on Sasakian manifolds. Advances in Theoretical and Mathematical Physics, 24(2), 259-278.
  Biswas, Indranil; Dumitrescu, Sorin & Schumacher, Georg
  
• Deformation theory of holomorphic Cartan geometries. Indagationes Mathematicae, 31(3), 512-524.
  Biswas, Indranil; Dumitrescu, Sorin & Schumacher, Georg
  
• Kähler Forms for Families of Calabi–Yau Manifolds. Publications of the Research Institute for Mathematical Sciences, 56(1), 1-13.
  Braun, Matthias; Choi, Young-Jun & Schumacher, Georg
  
• L^2-cohomology for affine spaces and an application to monads. Rocky Mountain Journal of Mathematics, 50(5).
  Buchdahl, Nicholas P. & Schumacher, Georg
  
• Polystahility and the Hitchin-Kohayashi correspondence. arXiv:2002.03548
  Schumacher, Georg & Buchdahl, Nicholas
  
• An analytic application of Geometric Invariant Theory. Journal of Geometry and Physics, 165(2021, 7), 104237.
  Buchdahl, Nicholas & Schumacher, Georg
  
• Extension of the curvature form of the relative canonical line bundle on families of Calabi–Yau manifolds and applications. Annales de l'Institut Fourier, 71(1), 393-406.
  Choi, Young-Jun & Schumacher, Georg
  
• Positivity of direct images of fiberwise Ricci-flat metrics on Calabi-Yau fibrations. Transactions of the American Mathematical Society, 374(6), 4267-4292.
  Braun, Matthias; Choi, Young-Jun & Schumacher, Georg
  
• The Weil–Petersson current on Douady spaces. Mathematische Nachrichten, 294(4), 638-656.
  Axelsson, Reynir & Schumacher, Georg
  
• An analytic application of Geometric Invariant Theory II: Coarse moduli spaces. Journal of Geometry and Physics, 175(2022, 5), 104467.
  Buchdahl, Nicholas & Schumacher, Georg
  
• Deformation theory of holomorphic Cartan geometries, II. Complex Manifolds, 9(1), 52-64.
  Biswas, Indranil; Dumitrescu, Sorin & Schumacher, Georg
  
• Polystable bundles and representations of their automorphisms. Complex Manifolds, 9(1), 78-113.
  Buchdahl, Nicholas & Schumacher, Georg
  
• Estimates for the average scalar curvature of the Weil–Petersson metric on the moduli space $${\overline{{{\mathcal {M}}} }}_g$$. manuscripta mathematica, 174(3-4), 807-813.
  Schumacher, Georg & Trapani, Stefano
  
• Weil–Petersson forms for families of polystable bundles over compact Kähler manifolds. International Journal of Mathematics, 34(13).
  Buchdahl, Nicholas & Schumacher, Georg