ALGEBRAIC GEOMETRY (1) Consider the function y in the function
... Explain the results geometrically. Answer: three affine points, two of them complex (and invisible in the real picture). In addition, there’s one point of intersection at infinity since both curves go to infinity in the direction of the y-axis. (5) Find all points on the projective closure of the cu ...
... Explain the results geometrically. Answer: three affine points, two of them complex (and invisible in the real picture). In addition, there’s one point of intersection at infinity since both curves go to infinity in the direction of the y-axis. (5) Find all points on the projective closure of the cu ...
PHƯƠNG PHÁP PHÁT HIỆN CÁC ĐỊNH LÍ MỚI VỀ HÌNH HỌC
... in particular is all of our dream. That’s reason why, researchers give not only nice and beautiful theorems but also founded methods of new geometric theorems. These are two important factors of researchers in this era. In fact, there are a lot of founded methods of new theorems such as affine-homog ...
... in particular is all of our dream. That’s reason why, researchers give not only nice and beautiful theorems but also founded methods of new geometric theorems. These are two important factors of researchers in this era. In fact, there are a lot of founded methods of new theorems such as affine-homog ...
Theorem 1. (Exterior Angle Inequality) The measure of an exterior
... Proof: By Lemma 2, the angle sum of 4ABC ≤ 180◦ and the angle sum of 4ACD ≤ 180◦ . If both of these inequalities were equalities we would have m∠1 + m∠2 + m∠B + m∠D + m∠3 + m∠4 = 360, in which case the angle sum of 4ABD = m∠1 + m∠2 + m∠B + m∠D = 360 − m∠3 − m∠4 = 180◦ , contradicting our hypothesis. ...
... Proof: By Lemma 2, the angle sum of 4ABC ≤ 180◦ and the angle sum of 4ACD ≤ 180◦ . If both of these inequalities were equalities we would have m∠1 + m∠2 + m∠B + m∠D + m∠3 + m∠4 = 360, in which case the angle sum of 4ABD = m∠1 + m∠2 + m∠B + m∠D = 360 − m∠3 − m∠4 = 180◦ , contradicting our hypothesis. ...
Riemann–Roch theorem
The Riemann–Roch theorem is an important theorem in mathematics, specifically in complex analysis and algebraic geometry, for the computation of the dimension of the space of meromorphic functions with prescribed zeroes and allowed poles. It relates the complex analysis of a connected compact Riemann surface with the surface's purely topological genus g, in a way that can be carried over into purely algebraic settings.Initially proved as Riemann's inequality by Riemann (1857), the theorem reached its definitive form for Riemann surfaces after work of Riemann's short-lived student Gustav Roch (1865). It was later generalized to algebraic curves, to higher-dimensional varieties and beyond.