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Priska Jahnke

Publications and source records attributed to Priska Jahnke.

15 recordsLinked to original sources
arXiv2015

Projective uniformization, extremal Chern classes and quaternionic Shimura curves

Projective structures on compact real manifolds are classical objects in real differential geometry. Complex manifolds with a holomorphic projective structure on the other hand form a special class as soon as the dimension is greater than one. In the Kähler Einstein case, projective space, tori and ball quotients are essentially the only examples. They can be described purely in terms of Chern class conditions. We give a complete classification of all projective manifolds carrying a projective structure. The only additional examples are modular abelian families over quaternionic Shimura curves. They can also be described purely in terms of Chern class conditions.

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arXiv2011

Semistability of restricted tangent bundles and a question of I. Biswas

Let M be a complex projective manifold with the property that for any compact Riemann surface C and holomorphic map f: C -> M the pullback of the tangent bundle of M is semistable. We prove that in this case M is a curve or a finite etale quotient of an abelian variety answering a conjecture of I. Biswas.

math.AG↗
arXiv2010

Splitting submanifolds of families of fake elliptic curves

Let N a compact complex submanifold of a compact complex manifold M. We say N splits in M, if the holomorphic tangent bundle sequence splits holomorphically. By a result of Mok a splitting submanifold of a Kaehler Einstein manifold with a projective structure is totally geodesic. The classification of all splitting submanifolds of families of fake elliptic curves given here completes the case of threefolds M with a projective structure by a previous result of the authors.

math.AG↗
arXiv2007

Threefolds with big and nef anticanonical bundles II

In continuation of our paper in Math. Ann. 333 we classify smooth complex projective threefolds X with -K_X big and nef but not ample and Picard number 2, whose anticanonical map is small. We assume also that the Mori contraction of X and of its flop are not both birational.

math.AG↗
arXiv2006

Almost del Pezzo manifolds

We classify almost del Pezzo manifolds in arbitrary dimension n, i.e., projective manifolds X with big and nef anticanonical bundle -K_X, such that -K_X is divisible by n-1.

math.AG↗
arXiv2005

Threefolds with big and nef anticanonical bundles I

We start the classification of smooth projective threefolds X whose anticanonical bundles -K_X are big and nef but not ample. In this paper we treat the case b_2(X) = 2 and the morphism associated with the base point free linear system |-mK_X|, m>>0, is divisorial.

math.AG↗
arXiv2004

Submanifolds with splitting tangent sequence

In the late 50's A. Van de Ven stated that the only compact submanifolds with splitting tangent sequence of the projective space are linear subspaces. In this paper a classification of all submanifolds with splitting tangent sequence of some further classes of (homogeneous) manifolds is given, like quadrics or abelian varieties.

math.AG↗
arXiv2002

Splitting jet sequences

The consequences of the splitting of higher jet sequences of vector bundles on a compact complex (Kaehler) manifold are studied, proving an infinitesimal convers to a result of I.Biswas.

math.AG↗
arXiv2002

On manifolds with holomorphic normal projective connections

The authors give a complete classification of projective threefolds admitting a holomorphic normal projective connection. Moreover, they prove a general structure theorem on complex projective manifolds admitting a holomorphic normal projective connection, saying in particular, that any such manifold is either the projective space or minimal in the sense of Mori.

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