Course Outline: Following the department syllabus from Algebraic Geometry by Robin Hartschorne chapters II and III. I will plan to cover approximately one section each week looking at something like 1-5 of chapter II on schemes and 4-7 on chapter III on cohomology. The last few lectures covered Bertini's hyperplane theorem (Thm II.8.18) and the nonsingular case of Serre duality (Cor III.7.7) drawing on Ext functors in section III.6 and effacibility from section III.1. The final week will look at flat families and Hilbert polynomials (Thm III.9.9) drawing on the homework problem III.5.2 and consider the example of the j-curve of elliptic curves in section IV.4 which can be viewed as an example of a family of divisors as in Example III.9.8.5 in the quadric surface from Exercise III.5.6.

HW1 1.1, 1.17, 1.18, 2.1 from chapter II of the text. Due Friday April 19.

HW2 2.2, 2.7, 2.10, 2.19 from chapter II of the text. Due Friday April 26.

HW3 2.16.a, 2.17.a, 3.11.ac from chapter II of the text. Due Friday May 3.

HW4 4.1, 4.8, 4.9 from chapter II of the text. Due Friday May 10.

HW5 5.1.d, 5.5, 5.7 from chapter II of the text. Due Friday May 17.

HW6 4.1, 4.3, 4.6, 4.7 from chapter III of the text. Due Friday May 24.

HW7 5.1, 5.2, 6.2, 6.7 from chapter III of the text. Due Friday May 31.