Ri-Xiang Chen

Ri-Xiang Chen
Ph.D. (2011) Cornell University

First Position

Instructor at Shantou University in Guangdong, China


Hilbert Functions and Free Resolutions


Research Area:
commutative algebra and algebraic geometry

Abstract: Hilbert functions and free resolutions are central concepts in the field of commutative algebra. In chapter 3 we prove some cases of the well-known Eisenbud-Green-Harris Conjecture. This conjecture characterizes the Hilbert functions of graded ideals containing a regular sequence in the polynomial ring. In chapter 4 we study the Hilbert functions of graded ideals in toric rings. We prove that Macaulay's Theorem holds for some projective monomial curves, and show that Macaulay's Theorem does not hold for all projective monomial curves. In the last chapter we construct explicitly the minimal free resolutions of linear edge ideals.