Resumen de Multi-Rees algebras of strongly stable ideals

Selvi Kara, Kuei-Nuan Lin, Gabriel Sosa

• We prove that the multi-Rees algebra of a collection of strongly stable ideals is of fiber type. In particular, we provide a Gröbner basis for its defining ideal as a union of a Gröbner basis for its special fiber and binomial syzygies. We also study the Koszulness of based on parameters associated to the collection. Furthermore, we establish a quadratic Gröbner basis of the defining ideal of where each of the strongly stable ideals has two quadric Borel generators. As a consequence, we conclude that this multi-Rees algebra is Koszul.