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Recent results on the Kobayashi and Green-Griffiths-Lang conjectures
The study of entire holomorphic curves contained in projective algebraic varieties is intimately related to fascinating questions of geometry and...
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On the locus of higher order jets of entire curves in complex projective varieties
For a given complex projective variety, the existence of entire curves is strongly constrained by the positivity properties of the cotangent bundle....
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Non-reductive geometric invariant theory and hyperbolicity
The Green–Griffiths–Lang and Kobayashi hyperbolicity conjectures for generic hypersurfaces of polynomial degree are proved using intersection theory...
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Optimal \(L^2\) Extension for Holomorphic Vector Bundles with Singular Hermitian Metrics
In the present paper, we study the properties of singular Nakano positivity of singular Hermitian metrics on holomorphic vector bundles, and...
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References
Abstract not available
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Picard theorems for moduli spaces of polarized varieties
As a result of our study of the hyperbolicity of the moduli space of polarized manifold, we give a general big Picard theorem for a holomorphic curve...
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The Demailly system for a direct sum of ample line bundles on Riemann surfaces
We prove that a system of equations introduced by Demailly (to attack a conjecture of Griffiths) has a smooth solution for a direct sum of ample line...
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Demailly’s notion of algebraic hyperbolicity: geometricity, boundedness, moduli of maps
Demailly’s conjecture, which is a consequence of the Green–Griffiths–Lang conjecture on varieties of general type, states that an algebraically...
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Intersection Cohomology and Severi Varieties
Let \(X^{2n}\subseteq \mathbb {P}^N\) be a smooth projective variety....
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Chen-Jiang decompositions for projective varieties, without Hodge modules
We give a new proof of a theorem by Pareschi, Popa and Schnell that the direct image of the canonical bundle of a smooth projective variety along a...
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Recent Geometric Flows in Multi-orientation Image Processing via a Cartan Connection
Applications of geometric flows to multi-orientation image processing require the choice of an (affine) connection on the Lie group G of...
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Algebraic hyperbolicity of very general surfaces
Recently, Haase and Ilten initiated the study of classifying algebraically hyperbolic surfaces in toric threefolds. We complete this classification...
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Counterexamples to the MMP for 1-foliations in positive characteristic
We show that many statements of the Minimal Model Program, including the cone theorem, the base point free theorem and the existence of Mori fibre...
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Chapter X: Arakelov Theory on Shimura Varieties
The generalization of Arakelov Theory to higher dimensions by Gillet and Soulé is well suited to study vector bundles with smooth hermitian metrics....
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Asymptotic expansions of complete Kähler-Einstein metrics with finite volume on quasi-projective manifolds
We give an elementary proof to the asymptotic expansion formula of Rochon and Zhang (2012) for the unique complete Kähler-Einstein metric of Cheng...
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A note on a Griffiths-type ring for complete intersections in Grassmannians
We calculate a Griffiths-type ring for smooth complete intersections in Grassmannians. This is the analogue of the classical Jacobian ring for...