9 papers · 1 filter
Koszul multi-Rees algebras of principal -Borel Ideals
Michael DiPasquale, Babak Jabbar Nezhad
Given a monomial in a polynomial ring and a subset of the variables of the polynomial ring, the principal -Borel ideal generated by is the ideal generated by all mon…
On resurgence via asymptotic resurgence
Michael DiPasquale, Ben Drabkin
The resurgence and asymptotic resurgence of an ideal in a polynomial ring are two statistics which measure the relationship between its regular and symbolic powers. We address two…
Bivariate Semialgebraic Splines
Michael DiPasquale, Frank Sottile
Semialgebraic splines are bivariate splines over meshes whose edges are arcs of algebraic curves. They were first considered by Wang, Chui, and Stiller. We compute the dimension of…
Asymptotic resurgence via integral closures
Michael DiPasquale, Christopher A. Francisco, Jeffrey Mermin +1
Given an ideal in a polynomial ring, we show that the asymptotic resurgence studied by Guardo, Harbourne, and Van Tuyl can be computed using integral closures. As a consequence, th…
Free Multiplicities on the moduli of
Michael DiPasquale, Max Wakefield
In this note we study the freeness of the module of derivations on all moduli of the arrangement with multiplicities. We use homological techniques stemming from work of Yuzv…
The Rees algebra of a two-Borel ideal is Koszul
Michael DiPasquale, Christopher A. Francisco, Jeffrey Mermin +2
Let and be two monomials of the same degree, and let be the smallest Borel ideal containing and . We show that the toric ring of is Koszul by constructing a…