Skip directly to content

Minimize RSR Award Detail

Research Spending & Results

Award Detail

Awardee:TRUSTEES OF PRINCETON UNIVERSITY, THE
Doing Business As Name:Princeton University
PD/PI:
  • Chenyang Xu
  • (857) 253-8748
  • chenyang@princeton.edu
Award Date:09/20/2021
Estimated Total Award Amount: $ 330,000
Funds Obligated to Date: $ 133,960
  • FY 2020=$65,674
  • FY 2021=$65,078
  • FY 2019=$3,208
Start Date:06/01/2021
End Date:05/31/2022
Transaction Type:Grant
Agency:NSF
Awarding Agency Code:4900
Funding Agency Code:4900
CFDA Number:47.049
Primary Program Source:040100 NSF RESEARCH & RELATED ACTIVIT
Award Title or Description:K-stability and Higher Dimensional Geometry
Federal Award ID Number:2153115
DUNS ID:002484665
Parent DUNS ID:002484665
Program:ALGEBRA,NUMBER THEORY,AND COM
Program Officer:
  • Sandra Spiroff
  • (703) 292-8069
  • sspiroff@nsf.gov

Awardee Location

Street:Off. of Research & Proj. Admin.
City:Princeton
State:NJ
ZIP:08544-2020
County:Princeton
Country:US
Awardee Cong. District:12

Primary Place of Performance

Organization Name:Princeton University
Street:Fine Hall
City:Princeton
State:NJ
ZIP:08544-1000
County:Princeton
Country:US
Cong. District:12

Abstract at Time of Award

The Principal Investigator (PI) will study varieties. Varieties are defined as the set of solutions of systems of polynomial equations. They are fairly easy to compute and Nash proved every space can be well approximated by varieties. The main aim of the project is to understand how varieties vary if we change the coefficients of the defining polynomial equations, especially for the ones which are positively curved. Such varieties are called Fano varieties. In particular the research will try to understand situations when a family of Fano varieties degenerates to one with singularities. The PI intends to prove that among all Fano varieties, the K-polystable ones can be parametrised by a universal space, called moduli space. As part of the this project, the PI aims to show the moduli space is Hausdorff and compact. The PI aims to understand which Fano varieties are K-semistable by understanding concrete examples as well as some general phenomena. The PI aims to understand the degeneration of Calabi-Yau manifolds, through the interplay between birational and non-archimedean geometry. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

For specific questions or comments about this information including the NSF Project Outcomes Report, contact us.