On abelian families and holomorphic normal projective connections

We prove Chern class equalities for abelian families with a holomorphic normal projective connection.Comment: 7 pages, LaTeX2

Terminal Fano threefolds and their smoothings

We study smoothings of Fano threefolds. We prove that the Picard number remains constant in the case of terminal Gorenstein singularities.Comment: 6 pages, LaTeX2

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.Comment: 19 pages, LaTeX2

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.Comment: 11 pages, LaTeX2

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 K\"ahler 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.Comment: 19 pages. arXiv admin note: text overlap with arXiv:0903.457

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.Comment: 13 page

Locally DD-optimal Designs for a Wider Class of Non-linear Models on the kk-dimensional Ball with applications to logit and probit models

In this paper we extend the results of Radloff and Schwabe (2018), which could be applied for example to Poisson regression, negative binomial regression and proportional hazard models with censoring, to a wider class of non-linear multiple regression models. This includes the binary response models with logit and probit link besides other. For this class of models we derive (locally) $D$-optimal designs when the design region is a $k$-dimensional ball. For the corresponding construction we make use of the concept of invariance and equivariance in the context of optimal designs as in our previous paper. In contrast to the former results the designs will not necessarily be exact designs in all cases. Instead approximate designs can appear. These results can be generalized to arbitrary ellipsoidal design regions.Comment: 11 pages, 7 figures. arXiv admin note: text overlap with arXiv:1806.0027

Holomorphic normal projective connections on projective manifolds

We study projective manifolds M admitting a (flat) holomorphic normal projective connection and show that the Iitaka fibration (up to etale coverings) defines a smooth abelian group scheme structure on M.Comment: 18 pages, LaTeX2

Gorenstein Fano threefolds with base points in the anticanonical system

We classify all Gorenstein Fano threefolds with at worst canonical singularities for which the anticanonical system has a nonempty base locus.Comment: 14 pages, LaTeX2e; final version, to appear in Comp. Mat

Projective Threefolds with Holomorphic Conformal Structure

The authors give a complete classification of projective threefolds admitting a holomorphic conformal structure. A Corollary is the complete list of projective threefolds, whose tangent bundle is a symmetric square.Comment: 10 pages, LaTeX2