Hyperbolicity related problems for complete intersection varieties

DOI10.1112/S0010437X13007458zbMath1386.32025arXiv1101.3394OpenAlexW3105465671MaRDI QIDQ5415170

Damian Brotbek

Publication date: 12 May 2014

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1101.3394

zbMATH Keywords

complete intersectionsample cotangent bundlejet differential equations

Mathematics Subject Classification ID

Vector bundles on surfaces and higher-dimensional varieties, and their moduli (14J60) Complete intersections (14M10) Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials (14F10) Sheaves and cohomology of sections of holomorphic vector bundles, general results (32L10) Hyperbolic and Kobayashi hyperbolic manifolds (32Q45)

Related Items (13)

Complete intersection varieties with ample cotangent bundles ⋮ On the ampleness of the cotangent bundles of complete intersections ⋮ Symmetric differential forms on complete intersection varieties and applications ⋮ Fiber integration on the Demailly tower ⋮ Effective bounds on ampleness of cotangent bundles ⋮ Families of explicit quasi-hyperbolic and hyperbolic surfaces ⋮ Boundedness in families with applications to arithmetic hyperbolicity ⋮ Demailly's notion of algebraic hyperbolicity: geometricity, boundedness, moduli of maps ⋮ Compact Kähler manifolds homotopic to negatively curved Riemannian manifolds ⋮ On the hyperbolicity of general hypersurfaces ⋮ Symmetric differentials and the fundamental group ⋮ Rationality in Differential Algebraic Geometry ⋮ A remark on the intersection of plane curves

Cites Work

• On a conjecture of Clemens on rational curves on hypersurfaces
• Positive polynomials for ample vector bundles
• Effective algebraic degeneracy
• Existence of global invariant jet differentials on projective hypersurfaces of high degree
• On the density of ratios of Chern classes of algebraic surfaces
• Ample vector bundles, Chern classes, and numerical criteria
• Low pole order frames on vertical jets of the universal hypersurface
• Families of hypersurfaces of large degree
• Weak analytic hyperbolicity of generic hypersurfaces of high degree in \(\mathbb P^4\)
• Vector fields on the total space of hypersurfaces in the projective space and hyperbolicity
• Logarithmic Vector Fields and Hyperbolicity
• Varieties with ample cotangent bundle
• Differential equations on complex projective hypersurfaces of low dimension
• On the Chern numbers of surfaces of general type

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