92 citations · 473 across the 45 of their papers we have counts for
17 papers · 1 filter
A short proof of the Hanlon-Hicks-Lazarev Theorem
Michael K. Brown, Daniel Erman
We give a short, new proof of a recent result of Hanlon-Hicks-Lazarev about toric varieties. As in their work, this leads to a proof of a conjecture of Berkesch-Erman-Smith on virt…
Tate resolutions on toric varieties
Michael K. Brown, Daniel Erman
We develop an analogue of Eisenbud-Floystad-Schreyer's Tate resolutions for toric varieties. Our construction, which is given by a noncommutative analogue of a Fourier- Mukai trans…
Tate Resolutions on Products of Projective Spaces: Cohomology and Direct Image Complexes
Daniel Erman, David Eisenbud, Frank-Olaf Schreyer
We describe the Macaulay2 package TateOnProducts and its capabilities, which include computing cohomology tables and Beilinson monads of sheaves on products of projective spaces an…
Strength and Hartshorne's Conjecture in high degree
Daniel Erman, Steven V Sam, Andrew Snowden
Hartshorne conjectured that a smooth, codimension c subvariety of n-dimensional projective space must be a complete intersection, whenever c is less than n/3. We prove this in the…
An equivariant Hilbert basis theorem
Daniel Erman, Steven V Sam, Andrew Snowden
We prove a version of the Hilbert basis theorem in the setting of equivariant algebraic geometry: given a group G acting on a finite type morphism of schemes X -> S, if S is topolo…
Supernatural analogues of Beilinson monads
Daniel Erman, Steven V Sam
We use supernatural bundles to build GL-equivariant resolutions supported on the diagonal of P^n x P^n, in a way that extends Beilinson's resolution of the diagonal. We thus obtain…
Furstenberg sets and Furstenberg schemes over finite fields
Jordan S. Ellenberg, Daniel Erman
We give a lower bound for the size of a subset of containing a rich k-plane in every direction, a k-plane Furstenberg set. The chief novelty of our method is that w…
A quick proof of nonvanishing for asymptotic syzygies
Lawrence Ein, Daniel Erman, Robert Lazarsfeld
We give a quick new approach to the main cases of the nonvanishing theorems of first and third authors concerning the asymptotic behavior of the syzygies of a projective variety as…
Tate Resolutions for Products of Projective Spaces
David Eisenbud, Daniel Erman, Frank-Olaf Schreyer
We describe the Tate resolution of a coherent sheaf or complex of coherent sheaves on a product of projective spaces. Such a resolution makes explicit all the cohomology of all twi…
The Betti table of a high degree curve is asymptotically pure
Daniel Erman
We prove that asymptotically in the degree, the main term of the Boij--Söderberg decomposition of a high degree curve is a single pure diagram that only depends on the genus of the…
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…
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…
Gauss Composition for P^1, and the universal Jacobian of the Hurwitz space of double covers
Daniel Erman, Melanie Matchett Wood
We investigate the universal Jacobian of degree n line bundles over the Hurwitz stack of double covers of P^1 by a curve of genus g. Our main results are: the construction of a smo…
Secant varieties of P^2 x P^n embedded by O(1,2)
Dustin Cartwright, Daniel Erman, Luke Oeding
We describe the defining ideal of the rth secant variety of P^2 x P^n embedded by O(1,2), for arbitrary n and r at most 5. We also present the Schur module decomposition of the spa…
A syzygetic approach to the smoothability of zero-dimensional schemes
Daniel Erman, Mauricio Velasco
We consider the question of which zero-dimensional schemes deform to a collection of distinct points; equivalently, we ask which Artinian k-algebras deform to a product of fields.…
Hilbert schemes of 8 points
Dustin A. Cartwright, Daniel Erman, Mauricio Velasco +1
The Hilbert scheme H^d_n of n points in A^d contains an irreducible component R^d_n which generically represents n distinct points in A^d. We show that when n is at most 8, the Hil…