213 research outputs found
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
On the moduli of degree 4 Del Pezzo surfaces
We study irreducibility of families of degree 4 Del Pezzo surface fibrations
over curves.Comment: 36 page
The Abel-Jacobi map for a cubic threefold and periods of Fano threefolds of degree 14
The Abel-Jacobi maps of the families of elliptic quintics and rational
quartics lying on a smooth cubic threefold are studied. It is proved that their
generic fiber is the 5-dimensional projective space for quintics, and a smooth
3-dimensional variety birational to the cubic itself for quartics. The paper is
a continuation of the recent work of Markushevich-Tikhomirov, who showed that
the first Abel-Jacobi map factors through the moduli component of stable rank 2
vector bundles on the cubic threefold with Chern numbers
obtained by Serre's construction from elliptic quintics, and that the
factorizing map from the moduli space to the intermediate Jacobian is \'etale.
The above result implies that the degree of the \'etale map is 1, hence the
moduli component of vector bundles is birational to the intermediate Jacobian.
As an applicaton, it is shown that the generic fiber of the period map of Fano
varieties of degree 14 is birational to the intermediate Jacobian of the
associated cubic threefold.Comment: Latex, 28 page
The curve of lines on a prime Fano threefold of genus 8
We show that a general prime Fano threefold X of genus 8 can be reconstructed
from the pair , where is its Fano curve of lines and
is the theta-characteristic which gives a natural embedding
\Gamma \subset \matbb{P}^5.Comment: 24 pages, misprints corrected, to appear in International Journal of
Mathematic
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