- Some Properties of Quantum Cohomology Determined by Positivity
- Project Year:
2017
- REU Student (s):
Nalinpat Ponoi | Prince of Songkla University (Thailand)
- Student 1 Institution:
Prince of Songkla University
- Project Mentor:
Anders Buch
- Project Mentor Area:
Mathematics
- Project Abstract:
We study the multiplicative of a (small) quantum cohomology ring which is encoded by Gromov-Witten invariants.
The multiplicative structure of the cohomology ring is rather complicated.
In this work, we use the Pieri formula to work on the special cases.
Since Gromov-Witten invariants are positive integers, a conjecture of Buch states that this fact determines some properties in quantum cohomology.
He also proves that it is true for the Grassmann variety Gr(2,n).
We try to prove that this is also true for Gr(m,n) when m>2.
