Hilbert schemes with two Borel-fixed points in arbitrary characteristic

Abstract

We extend the recent classification of Hilbert schemes with two Borel-fixed points to positive characteristic. We accomplish this by synthesizing Reeves’ algorithm for generating strongly stable ideals with the characteristic free properties of Borel-fixed ideals and our previous work classifying Hilbert schemes with unique Borel-fixed points in any characteristic.

Keywords:

• Borel-fixed ideal
• classification
• Hilbert scheme
• positive characteristic
• strongly stable ideal

2020 Mathematics Subject Classification:

• 13A35
• 13C05
• 13C70
• 14C05
• 14G17

Acknowledgments

We thank Joachim Jelisiejew for pointing out the overlap between Ritvik Ramkumar’s work and our own, and Greg Smith for helpful suggestions. We thank Eran Nevo and The Hebrew University of Jerusalem for their support, as well as the Topology and Geometry Group at the University of Waterloo.