Plane Conics in Algebraic Geometry

نویسنده

  • ERIC YAO
چکیده

We first examine points and lines within projective spaces. Then we classify affine conics based on the classification of projective conics. Based on the parametrization of conics, we also prove two easy cases of Bézout’s Theorem. In the end we turn to the discussion of the space of conics and the notion of pencils of conics.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Conics on the Projective Plane

In this paper, we discuss a special property of conics on the projective plane and answer questions in enumerative algebraic geometry such as ”How many points determine a conic?” and ”How many conics do we expect to pass through m points and tangent to n lines?”

متن کامل

Enumerative Algebraic Geometry of Conics

1. INTRODUCTION. In 1848 Jakob Steiner, professor of geometry at the University of Berlin, posed the following problem [19]: Given five conics in the plane, are there any conics that are tangent to all five? If so, how many are there? Problems that ask for the number of geometric objects with given properties are known as enumera-tive problems in algebraic geometry. The tools developed to solve...

متن کامل

Splitting Root-Locus Plot into Algebraic Plane Curves

In this paper we show how to split the root-locus plot for an irreducible rational transfer function into several individual algebraic plane curves, like lines, circles, conics, etc. To achieve this goal we use results of a previous paper of the author to represent the Root Locus as an algebraic variety generated by an ideal over a polynomial ring, and whose primary decomposion allow us to isol...

متن کامل

LDPC codes generated by conics in the classical projective plane

We construct various classes of low-density parity-check codes using point-line incidence structures in the classical projective plane PG(2, q). Each incidence structure is based on the various point classes (internal, external) and line classes (skew, tangent, secant) created by the geometry of a conic in the plane. For each class, we prove various properties about dimension and minimum distan...

متن کامل

Object and motion recognition using the plane plus parallax displacement of conics

Parallax displacement is used to determine a relative 3D conic projective structure. This value is invariant between any number of views in time if the conic is not moving with respect to the plane of the homography. It can be used to determine conic correspondence between three simultaneous views. The corresponding conics may then be used to determine the epipolar geometry. This method of dete...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2014