MAT 614: Enumerative Geometry

Stony Brook            Fall 2007



Here are Notes on Mirror Symmetry (updated 12/12). They are in preparation; only Sections 1 and 3 are currently ready; I may add more in the future. Please let me know if you have any comments or corrections (however minor).

Here is general information about the course (updated 8/28), including a fairly detailed syllabus.


Course Instructor

Name: Aleksey Zinger     E-mail: azinger@math     Phone: 432-8618
Office: Math Tower 3-117     Office Hours: Wednesday 9-12 (9-10 may be in P-143)



Date TopicRead
9/5, W Course Overview; Review of Chern Classes, etc. [K]: Ch 1,2,4-6
[MS]: Ch 10,11,13,14
[Z1]: Sec 1,2.1,2.2,A.1,A.3,A.4
9/10, MCounting Lines in Projective Spaces
Schubert Calculus
[K]: Ch 7
[GH]: Ch 1, Sec 1
[MS]: Ch 14
9/12, WCounting Lines in Projective Hypersurfaces
9/17, Mno class
9/19, WPseudocycles and Integral Homology [Z2]
9/24, M
9/26, WCounting Low-Degree Curves in P2: Simple Cases [K]: Ch 2
[Z1]: Sec 2, Subs 3.2,3.5.1-3.5.3
10/1, M
10/3, WCounting Low-Degree Curves in Pn: Simple Cases [GH]: pp176,177
10/8, MDegenerate Contributions: Overview
and Computation in Simple Cases
[K]: Ch 8
[Z3]: Sec 3
10/10, W
10/15, MLocal Excess Intersection Approach:
Fairly General Case
[Z4]: Sec 2
10/17, W
10/22, MLocal Excess Intersection Approach:
Singular Spaces
[Z4]: Sec 2
10/24, WCounting Rational Plane Quartics [Z1]: Subs 3.4,3.5.6
10/29, MRecursion for Counts of Rational Curves in P2 [Z1]: Sec 4
10/31, WGromov-Witten Invariants: Simple Cases [K]: Ch 3
[RT]: Sec 1,2,10
11/5, M
11/7, W An Example of Obstruction Bundle in GW Theory
11/12, M GW-Invariants of General Symplectic Manifolds[FO],[LT]
11/14, W Calabi-Yau 3-Folds and GW-Invariants[P1]
11/19, M Mirror Symmetry for Genus 0 GWs of a Quintic
On Genus-0 GW-Invariants of Hypersurfaces
[P2]: Sec 3; [K]: Ch 9
[MirSym]: Sec 26.1,29.1,29.2
11/21, W no class (Friday schedule 9-5)
11/26, MEquivariant Cohomology Notes: Sec 1
[AB]: Sec 1-3
11/28, WProof of Atiyah-Bott Localization Theorem
12/3, M Localization Theorem and Stable Maps[MirSym]: Sec 27.0-27.5
12/5, Wno class
12/10, M Proof of Genus-0 Mirror Symmetry Notes: Subs 3.1-3.5, [MirSym]: Sec 29.1-29.3,30.3,30.4
12/12, WNotes: Subs 3.6-3.8, [MirSym]: Sec 29.4,30.1,30.2



This page is maintained by Aleksey Zinger.
Last modified: December 12, 2007.