176 research outputs found
Intersections of the Hermitian Surface with irreducible Quadrics in even Characteristic
We determine the possible intersection sizes of a Hermitian surface with an irreducible quadric of sharing at least a
tangent plane at a common non-singular point when is even.Comment: 20 pages; extensively revised and corrected version. This paper
extends the results of arXiv:1307.8386 to the case q eve
Intersections of the Hermitian surface with irreducible quadrics in , odd
In , with odd, we determine the possible intersection sizes of
a Hermitian surface and an irreducible quadric
having the same tangent plane at a common point .Comment: 14 pages; clarified the case q=
Szemer\'edi--Trotter-type theorems in dimension 3
We estimate the number of incidences in a configuration of lines and
points in dimension 3. The main term is if we work over the real or
complex numbers but over finite fields. Both of these are optimal,
aside from a multiplicative constant that is at most 5.Comment: This paper supersedes arXiv:1404.4613. Version2: references updated
and small changes made. arXiv admin note: substantial text overlap with
arXiv:1404.4613 Version 3: Many changes and a new section added on ruled
surface
Intersection sets, three-character multisets and associated codes
In this article we construct new minimal intersection sets in
sporting three intersection numbers with hyperplanes; we
then use these sets to obtain linear error correcting codes with few weights,
whose weight enumerator we also determine. Furthermore, we provide a new family
of three-character multisets in with even and we
also compute their weight distribution.Comment: 17 Pages; revised and corrected result
On the monodromy of the moduli space of Calabi-Yau threefolds coming from eight planes in
It is a fundamental problem in geometry to decide which moduli spaces of
polarized algebraic varieties are embedded by their period maps as Zariski open
subsets of locally Hermitian symmetric domains. In the present work we prove
that the moduli space of Calabi-Yau threefolds coming from eight planes in
does {\em not} have this property. We show furthermore that the
monodromy group of a good family is Zariski dense in the corresponding
symplectic group. Moreover, we study a natural sublocus which we call
hyperelliptic locus, over which the variation of Hodge structures is naturally
isomorphic to wedge product of a variation of Hodge structures of weight one.
It turns out the hyperelliptic locus does not extend to a Shimura subvariety of
type III (Siegel space) within the moduli space. Besides general Hodge theory,
representation theory and computational commutative algebra, one of the proofs
depends on a new result on the tensor product decomposition of complex
polarized variations of Hodge structures.Comment: 26 page
Stability of restrictions of cotangent bundles of irreducible Hermitian symmetric spaces of compact type
It is known that the cotangent bundle of an irreducible Hermitian
symmetric space of compact type is stable. Except for a few obvious
exceptions, we show that if is a complete intersection such that
is surjective, then the restriction is
stable. We then address some cases where the Picard group increases by
restriction.Comment: Results and exposition improve
Signature Sequence of Intersection Curve of Two Quadrics for Exact Morphological Classification
We present an efficient method for classifying the morphology of the
intersection curve of two quadrics (QSIC) in PR3, 3D real projective space;
here, the term morphology is used in a broad sense to mean the shape,
topological, and algebraic properties of a QSIC, including singularity,
reducibility, the number of connected components, and the degree of each
irreducible component, etc. There are in total 35 different QSIC morphologies
with non-degenerate quadric pencils. For each of these 35 QSIC morphologies,
through a detailed study of the eigenvalue curve and the index function jump we
establish a characterizing algebraic condition expressed in terms of the Segre
characteristics and the signature sequence of a quadric pencil. We show how to
compute a signature sequence with rational arithmetic so as to determine the
morphology of the intersection curve of any two given quadrics. Two immediate
applications of our results are the robust topological classification of QSIC
in computing B-rep surface representation in solid modeling and the derivation
of algebraic conditions for collision detection of quadric primitives
-Intersection sets in and two-character multisets in
In this article we construct new minimal intersection sets in
with respect to hyperplanes, of size and multiplicity , where
rt \in \ q^2r-3-q^(3r-4)/2, q^2r-3-q^r-2\rqPG(3,q^2)AG(r,q^2)$ satisfying the opposite of the algebraic conditions required in [1]
for quasi--Hermitian varieties
Maximum number of points on intersection of a cubic surface and a non-degenerate Hermitian surface
In 1991 S{\o}rensen proposed a conjecture for the maximum number of points on
the intersection of a surface of degree and a non-degenerate Hermitian
surface in \PP^3(\Fqt). The conjecture was proven to be true by Edoukou in
the case when . In this paper, we prove that the conjecture is true for
and . We further determine the second highest number of rational
points on the intersection of a cubic surface and a non-degenerate Hermitian
surface. Finally, we classify all the cubic surfaces that admit the highest and
second highest number of points in common with a non-degenerate Hermitian
surface. This classifications disproves one of the conjectures proposed by
Edoukou, Ling and Xing
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