Math 7280: Algebraic Ceometry I

Fall  2005


Course description

Lecture Notes

1.  Algebraic Sets (notes by M. Bakhova) (pdf)
2.   Noetherian rings and modules (J. Culbertson) (pdf)
3.   V-I correspondence (M. Bennett) (pdf)
4.  Nullstellensatz (C. Egedy) (pdf)
5.  Morphisms (A. Lowrance)  (pdf)
6.  Zariski topology (J. Jean) (pdf)
7.  Examples; SINGULAR (P. Maciak) (pdf)
8.  More examples (B. Dribus)(pdf)
9.  Localization; local rings (K. Morris) (pdf)
10. Integral extensions (G. Tripathi)  (pdf)
11. Proof of the NSZ (R. Sutherland)
(pdf)
12. Projective space () ()
13. Projective V-I (M. Vega) (pdf)
14. Projective closure (M. Bakhova)  (pdf)
15.  Rational functions; regular functions (M. Bennett)(pdf)
16.  Morphisms I (J. Culbertson) (pdf)
17.  Morphisms II (B. Dribus)  (pdf)
18.  (Bi)rational maps; blowing-up (C. Egedy) (pdf
19.  Category theory I (J. Jean) (see lecture 32)
20.  Category theory II ()
21.  Sheaf theory I (A. Lowrance) (pdf)
22.  Sheaf theory II (P. Maciak) (pdf)
23.  Sheaf theory III (K. Morris) (pdf)
24.  Sheaf theory IV (R. Sutherland) (pdf)
25.  Spec(R) (G. Tripathi) (pdf)
26.  Schemes I (M. Vega) (pdf)
27.  Schemes II (M. Bakhova) (pdf)
28. 
Morphisms I (M. Bennett)(pdf)
29a. Morphisms II (J. Culbertson) (pdf)
29b. Morphisms II/Examples I (B. Dribus)  (pdf)
30.  Examples II (C. Egedy) (pdf)
31.  Glueing schemes (P. Maciak) (pdf)
32.  Representable functors (J. Jean)
(pdf)
33.  Functor of points; fiber product (A. Lowrance) (pdf)
34.  S-schemes; base-change (K. Morris) (pdf)
35.  S-schemes II (R. Sutherland)  (pdf)
36.  More examples (G. Tripathi) (pdf)
37.  Arithmetic schemes (M. Vega) (pdf)
38.  (Non)singularity (Hoffman)  (pdf)
39.  G-bundles (Hoffman) (pdf)
40.  Divisors and line bundles (Hoffman) (pdf)



Department of Mathematics
Louisiana State University
374 Lockett
Baton Rouge, LA, 70803

Phone: (225) 578-1575
Email: hoffman@math.lsu.edu