Calendar · Lecture Notes
MIT OpenCourseWare
Topics in Algebraic Geometry: Algebraic Surfaces
Art: Max Brückner (1860 – 1934), Brückner Vielflache Tafel 07 · Public domain
- Instructor
- Prof. Abhinav Kumar
- Term
- Spring 2008
- Level
- Graduate
- What's inside
- 1 lecture note · 24 other files · 3 web pages
- Materials open
- MIT OCW
About this course
Source: MIT OpenCourseWare 18.727 Topics in Algebraic Geometry: Algebraic Surfaces, Spring 2008, Prof. Abhinav Kumar — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: MIT's own listing order, section by section. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 23, 2026. How RedLectern is built.
Materials are grouped the way MIT organized them. A verified, course-wide order has not been established here.
Before you start
Prerequisites are not listed here. Check MIT's own syllabus for this course.
How this course was organized
What's here, and what isn't
- MIT's own materials here did not support a verified, course-wide order, so they are grouped by section instead.
Materials by section
Grouped by section, as MIT organized them. Not sequenced or ordered.
Lecture Notes
22 files
- Lecture 1 Download
- Lecture 2 Download
- Lecture 3 Download
- Lecture 4 Download
- Lecture 5 Download
- Lecture 6 Download
- Lecture 7 Download
- Lecture 8 Download
- Lecture 9 Download
- Lecture 10 Download
- Lecture 11 Download
- Lecture 12 Download
- Lecture 13 Download
- Lecture 14 Download
- Lecture 15 Download
- Lecture 16 Download
- Lecture 17 Download
- Lecture 18 Download
- Lecture 19 Download
- Lecture 20 Download
- Lecture 21 Download
- Lecture 22 Download
Assignments
Course outline
Calendar · Lecture Notes
Lecture 2: Linear equivalence, algebraic equivalence, numerical equivalence of divisors
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Lecture 3: Birational maps, rational maps, linear systems, properties of birational maps between surfaces
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Lecture 4: Birational maps (cont.)
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Lecture 5: Ruled surfaces I
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Lecture 6: Ruled surfaces II
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Lecture 7: Ruled surfaces III, rational surfaces
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Lecture 8: Linear systems, rational normal scrolls
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Lecture 9: Castelnuovo’s criterion for rationality
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Lecture 10: Picard variety
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Lecture 11: Albanese variety
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Lecture 12: Non-ruled and ruled surfaces
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Lecture 13: Classification of ruled surfaces
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Lecture 14: Elliptic and quasi-elliptic surfaces
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Lecture 15: Elliptic surfaces (cont.), Kodaira dimension 0
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Lecture 16: K3 surfaces
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Lecture 17: Enriques surfaces, bielliptic surfaces
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Lecture 18: Classification
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Lecture 19: Elliptic/quasi-elliptic fibrations I
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Lecture 20: Elliptic/quasi-elliptic fibrations II
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Lecture 21: Elliptic/quasi-elliptic fibrations III, classification
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Lecture 22: Classification (cont.)
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Lecture 23: Moduli
MIT OpenCourseWare, Prof. Abhinav Kumar, 18.727 Topics in Algebraic Geometry: Algebraic Surfaces, Spring 2008.
License: CC BY-NC-SA 4.0 · Edition: Spring 2008 · Open the original course on OCW ↗
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