92 citations · 473 across the 45 of their papers we have counts for
5 papers · 1 filter
Semiample Bertini theorems over finite fields
Daniel Erman, Melanie Matchett Wood
We prove a semiample generalization of Poonen's Bertini Theorem over a finite field that implies the existence of smooth sections for wide new classes of divisors. The probability…
Three flavors of extremal Betti tables
Christine Berkesch, Daniel Erman, Manoj Kummini
We discuss extremal Betti tables of resolutions in three different contexts. We begin over the graded polynomial ring, where extremal Betti tables correspond to pure resolutions. W…
Asymptotics of random Betti tables
Lawrence Ein, Daniel Erman, Robert Lazarsfeld
The purpose of this paper is twofold. First, we present a conjecture to the effect that the ranks of the syzygy modules of a smooth projective variety become normally distributed a…
Murphy's Law for Hilbert function strata in the Hilbert scheme of points
Daniel Erman
An open question is whether the Hilbert scheme of points of a high dimensional affine space satisfies Murphy's Law, as formulated by Vakil. In this short note, we instead consider…
Categorified duality in Boij-Söderberg Theory and invariants of free complexes
David Eisenbud, Daniel Erman
We present a robust categorical foundation for the duality theory introduced by Eisenbud and Schreyer to prove the Boij-Söderberg conjectures describing numerical invariants of syz…