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of 34
pro vyhledávání: '"Brotbek, Damian"'
Given a complex quasi-projective manifold $X$, a semisimple algebraic group $G$ defined over some non-archimedean local field $K$ and a Zariski dense representation $\varrho:\pi_1(X)\to G(K)$, we construct a $\varrho$-equivariant (pluri-)harmonic map
Externí odkaz:
http://arxiv.org/abs/2206.11835
Autor:
Brotbek, Damian, Brunebarbe, Yohan
We prove a Second Main Theorem type inequality for any log-smooth projective pair $(X,D)$ such that $X\setminus D$ supports a complex polarized variation of Hodge structures. This can be viewed as a Nevanlinna theoretic analogue of the Arakelov inequ
Externí odkaz:
http://arxiv.org/abs/2007.12957
Autor:
Brotbek, Damian, Deng, Ya
Publikováno v:
Geometric And Functional Analysis, In press
In this paper, we prove that in any projective manifold, the complements of general hypersurfaces of sufficiently large degree are Kobayashi hyperbolic. We also provide an effective lower bound on the degree. This confirms a conjecture by S. Kobayash
Externí odkaz:
http://arxiv.org/abs/1804.01719
Autor:
Brotbek, Damian, Deng, Ya
The aim of this work is to construct examples of pairs whose logarithmic cotangent bundles have strong positivity properties. These examples are constructed from any smooth n-dimensional complex projective varieties by considering the sum of at least
Externí odkaz:
http://arxiv.org/abs/1712.09887
Autor:
Brotbek, Damian
In 1970, Kobayashi conjectured that general hypersurfaces of sufficiently large degree in $P^n$ are hyperbolic. In this paper we prove that a general sufficiently ample hypersurface in a smooth projective variety is hyperbolic. To prove this statemen
Externí odkaz:
http://arxiv.org/abs/1604.00311
Autor:
Brotbek, Damian
Nous étudions différentes propriétés d'hyperbolicité pour les variétés intersection complète. Étant donnée une variété intersection complète lisse X ⊂ M dans une variété projective complexe lisse, nous démontrons que
Externí odkaz:
http://tel.archives-ouvertes.fr/tel-00677065
http://tel.archives-ouvertes.fr/docs/00/67/70/65/PDF/These.pdf
http://tel.archives-ouvertes.fr/docs/00/67/70/65/PDF/These.pdf
Autor:
Brotbek, Damian, Darondeau, Lionel
Any smooth projective variety contains many complete intersection subvarieties with ample cotangent bundles, of each dimension up to half its own dimension.
Comment: Reader-friendly version, to appear in Inventiones Mathematicae
Comment: Reader-friendly version, to appear in Inventiones Mathematicae
Externí odkaz:
http://arxiv.org/abs/1511.04709
Autor:
Brotbek, Damian
In this paper we study the cohomology of tensor products of symmetric powers of the cotangent bundle of complete intersection varieties in projective space. We provide an explicit description of some of those cohomology groups in terms of the equatio
Externí odkaz:
http://arxiv.org/abs/1406.7848
Autor:
Brotbek, Damian
We generalize a vanishing theorem for the cohomology of symmetric powers of the cotangent bundle of subvarieties of projective space due to Schneider. From this we deduce new vanishing results for Green-Griffiths jet differential bundles, generalizin
Externí odkaz:
http://arxiv.org/abs/1111.5324
Autor:
Brotbek, Damian
Publikováno v:
Compositio Math. 150 (2014) 369-395
In this paper we examine different problems regarding complete intersection varieties of high degree in a complex projective space. First we show how one can deduce hyperbolicity for generic complete intersection of high multidegree and high codimens
Externí odkaz:
http://arxiv.org/abs/1101.3394