Maximal families of nodal varieties with defect

In this paper we prove that a nodal hypersurface in P^4 with defect has at least (d-1)^2 nodes, and if it has at most 2(d-2)(d-1) nodes and d>6 then it contains either a plane or a quadric surface. Furthermore, we prove that a nodal double cover of P^3 ramified along a surface of degree 2d with defect has at least d(2d-1) nodes. We construct the largest dimensional family of nodal degree d hypersurfaces in P^(2n+2) with defect for d sufficiently large.Comment: v2: A proof for the Ciliberto-Di Gennaro conjecture is added (Section 5); Some minor corrections in the other sections. v3: some minor corrections in the abstract v4: The proof for the Ciliberto-Di Gennaro conjecture has been modified; The paper is split into two parts, the complete intersection case will be discussed in a different pape

Extremal elliptic surfaces & Infinitesimal Torelli

We describe in terms of the j-invariant all elliptic surfaces pi: X -> C with a section, such that h^{1,1}(X)=rank NS(X) and the Mordell-Weil group of pi is finite. We use this to give a complete solution to infinitesimal Torelli for elliptic surfaces with a section over P^1.Comment: 16 pages; 3rd version; small changes to the third and fourth sectio

Nodal surfaces with obstructed deformations

In this text we show that the deformation space of a nodal surface $X$ of degree $d$ is smooth and of the expected dimension if $d\leq 7$ or $d\geq 8$ and $X$ has at most $4d-5$ nodes. (The case $d\leq 7$ was previously covered by Alexandru Dimca by using different techniques.) For $d\geq 8$ we give explicit examples of nodal surfaces with $4d-4$ nodes, for which the tangent space to the deformation space has larger dimension than expected. We give a short discussion on the shape of the deformation space of surfaces of the form $f_1f_2+f_3^2f_4$, where $f_1$ is a linear form.Comment: v2: Added a reference to a similar result by Alexandru Dimca and a discussion on the difference between Dimca's result and ours v3: Expanded several argument

Zeta Functions of Monomial Deformations of Delsarte Hypersurfaces

Let $X_\lambda$ and $X_\lambda'$ be monomial deformations of two Delsarte hypersurfaces in weighted projective spaces. In this paper we give a sufficient condition so that their zeta functions have a common factor. This generalises results by Doran, Kelly, Salerno, Sperber, Voight and Whitcher [arXiv:1612.09249], where they showed this for a particular monomial deformation of a Calabi-Yau invertible polynomial. It turns out that our factor can be of higher degree than the factor found in [arXiv:1612.09249]

Design and implementation of a user-oriented speech recognition interface: the synergy of technology and human factors

The design and implementation of a user-oriented speech recognition interface are described. The interface enables the use of speech recognition in so-called interactive voice response systems which can be accessed via a telephone connection. In the design of the interface a synergy of technology and human factors is achieved. This synergy is very important for making speech interfaces a natural and acceptable form of human-machine interaction. Important concepts such as interfaces, human factors and speech recognition are discussed. Additionally, an indication is given as to how the synergy of human factors and technology can be realised by a sketch of the interface's implementation. An explanation is also provided of how the interface might be integrated in different applications fruitfully