1.Background and purpose：

In this course, we are going to give an introduction to the theory of algebraic surfaces, for motivated students who have some basic knowledge in algebra and geometry and would like to explore the beauty of algebraic geometry. Our purpose is to give a modern treatment of surface theory with minimal model theory and some other recent technique in mind, and leave the classical material as applications of general theory.

2.Outline：

(1) Review on algebraic curves/ compact Riemann surfaces

(2) Affine varieties, projective varieties (and some commutative algebra)

(3) Cohomology (and some homological algebra)

(4) Vanishing theorems

(5) Divisors and projective embedding

(6) Intersection theory.

(7) Riemann-Roch theorem.

(8) Cone of curves.

(9) Birational maps.

(10) Minimal models program (in general and in dimension two)

(11) Canonical bundle formula and pushforward of canonical sheaves

(12) Biraional classification.

(13) Pluricanonical maps and surfaces of general type.

(14) Elliptic surfaces.

(15) Surfaces with Kodaira dimension 0.

(16) K3 surfaces.

(17) Ruled and rational surfaces.

(18) Surface singularities.

3.Time and place：

Monday period 8,9 (15:30-17:20); Wednesday period 9 (16:30-17:20)

Astro-Math. Bldg. R. 440(Live streaming)

4.Credit：3

Course Live Streaming
Students Seminar on Toric Varieties