873 research outputs found
Nodal surfaces with obstructed deformations
In this text we show that the deformation space of a nodal surface of
degree is smooth and of the expected dimension if or
and has at most nodes. (The case was previously covered by
Alexandru Dimca by using different techniques.)
For we give explicit examples of nodal surfaces with 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 , where 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
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
Zeta Functions of Monomial Deformations of Delsarte Hypersurfaces
Let and 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]
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