Simon Fraser University
Engaging the World

Course Outlines

Spring 2022 - MATH 800 G100

Mathematics: Selected Topics (4)

Introduction to Complex Geometry

Class Number: 3310

Delivery Method: In Person

Overview

  • Course Times + Location:

    Jan 10 – Apr 11, 2022: Wed, 8:30–10:20 a.m.
    Burnaby

    Jan 10 – Apr 11, 2022: Fri, 10:30 a.m.–12:20 p.m.
    Burnaby

Description

COURSE DETAILS:

Introduction to Complex Geometry
 
In this introductory course, we will begin by learning the necessary basics of multivariate complex analysis. Armed with a good understanding of the local situation, we will then begin our study of complex manifolds. Topics discussed will include differential forms, (almost) complex structures, sheaves, and vector bundles. 
 
Specific topics covered:
 
Local theory (roughly 4 weeks)
  • Holomorphic functions in several variables
  • Complex structures
  • Differential forms
 
Complex manifolds (roughly 8 weeks)
  • Complex manifolds
  • Vector bundles
  • Divisors and line bundles
  • Projective space
  • Sheaves
  • Cech cohomology

Grading

  • 5 Written Problem Sets 20%
  • Project with Oral Examination 20%
  • Final Exam 60%

REQUIREMENTS:

A course in univariate complex functions, and background in the basics of topology.

Materials

REQUIRED READING:

Huybrechts, Daniel. Complex geometry. An introduction. Universitext. Springer-Verlag, Berlin, 2005. xii+309 pp. 
(available online through SFU library)

ISBN: 3-540-21290-6

Graduate Studies Notes:

Important dates and deadlines for graduate students are found here: http://www.sfu.ca/dean-gradstudies/current/important_dates/guidelines.html. The deadline to drop a course with a 100% refund is the end of week 2. The deadline to drop with no notation on your transcript is the end of week 3.

Registrar Notes:

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS

SFU’s Academic Integrity web site http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating.  Check out the site for more information and videos that help explain the issues in plain English.

Each student is responsible for his or her conduct as it affects the University community.  Academic dishonesty, in whatever form, is ultimately destructive of the values of the University. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the University. http://www.sfu.ca/policies/gazette/student/s10-01.html

TEACHING AT SFU IN SPRING 2022

Teaching at SFU in spring 2022 will involve primarily in-person instruction, with safety plans in place.  Some courses will still be offered through remote methods, and if so, this will be clearly identified in the schedule of classes.  You will also know at enrollment whether remote course components will be “live” (synchronous) or at your own pace (asynchronous).

Enrolling in a course acknowledges that you are able to attend in whatever format is required.  You should not enroll in a course that is in-person if you are not able to return to campus, and should be aware that remote study may entail different modes of learning, interaction with your instructor, and ways of getting feedback on your work than may be the case for in-person classes.

Students with hidden or visible disabilities who may need class or exam accommodations, including in the context of remote learning, are advised to register with the SFU Centre for Accessible Learning (caladmin@sfu.ca or 778-782-3112) as early as possible in order to prepare for the spring 2022 term.