Basic questions involve the study of the points of special interest like the singular points, the inflection points and the points at infinity. In these plane algebraic curves, a point of the plane belongs to an algebraic curve if its coordinates satisfy a given polynomial equation. Examples of the most studied classes of algebraic varieties are lines, circles, parabolas, ellipses, hyperbolas, cubic curves like elliptic curves, and quartic curves like lemniscates and Cassini ovals. The fundamental objects of study in algebraic geometry are algebraic varieties, which are geometric manifestations of solutions of systems of polynomial equations. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros.
Miles Reid, Undergraduate commutative algebra, CUP.Algebraic geometry is a branch of mathematics which classically studies zeros of multivariate polynomials. Miles Reid, Undergraduate algebraic geometry, CUP.įrances Kirwan, Complex algebraic curves, CUP. The main book for this course will be the book by Miles Reid, Quadric surfaces, blow ups, rational and birational maps. Hilbert Basis Theorem and the Nullstellensatz. Affine varieties and their rings of functions. Bezout's theorem (without proof) and its applications (Cayley-Bacharach theorem). This syllabus is for guidance purposes only :
#Algebraic geometry examples how to#
have learned how to formulate and prove basic statements about algebraic varieties in precise abstract algebraic languageĪssessment Information See 'Breakdown of Assessment Methods' and 'Additional Notes', above.Īdditional Information Academic description have increased their knowledge of finitely generated commutative rings and their fields of fractions, be familiar with explicit examples including plane curves, quadrics, cubic surfaces, Segre and Veronese embeddings, have knowledge of the basic affine and projective geometries, Students who successfully complete this module will : Summary of Intended Learning Outcomes A first course in algebraic geometry is a basic requirement for study in geometry, algebraic number theory or algebra at the MSc or PhD level. Programme Level Learning and Teaching Hours 2,ĭirected Learning and Independent Learning Hoursīreakdown of Assessment Methods (Further Info) Information for Visiting Students Pre-requisitesĭisplayed in Visiting Students Prospectus?ĭelivery period: 2013/14 Semester 2, Available to all students (SV1)īreakdown of Learning and Teaching activities (Further Info) Students MUST have passed: ( Algebra (MATH10021) AND Numbers & Rings (MATH10023) ) conics, plane curves, quadric surfaces.Įntry Requirements (not applicable to Visiting Students) Pre-requisites morphisms and rational maps between varieties, Hilbert Basis Theorem and the Nullstellensatz, We plan to cover Sections 1-5 and 7 from Reid's book (see Reading List below), which include : The focus will be on explicit concrete examples. In algebraic geometry: affine and projective varieties, and the mapsīetween them. This course will introduce the basic objects Motivation for further study through the introduction of minimalīackground material supplemented by a vast collection of examples. The goal of the course is to give a basic flavour of the subject as Spaces defined by polynomial equations in several variables.īesides providing crucial techniques and examples to many otherĪreas of geometry and topology, recent decades have seen remarkableĪpplications to representation theory, physics and to the construction of algebraic codes. It is a classical subject with a modern face that studies geometric Undergraduate Course: Algebraic Geometry (MATH11120) Course Outline SchoolĪlgebraic geometry studies geometric objects defined algebraically. DRPS : Course Catalogue : School of Mathematics : Mathematics
0 kommentar(er)
