46 citations · 182 across the 23 of their papers we have counts for
24 papers
Two New Extensions of Reider's Theorem on Algebraic Surfaces
Aaron Bertram, Jonathon Fleck, Liebo Pan +1
Reider's Theorem on the very ampleness of adjoint linear series on a complex projective algebraic surface is extended in two new directions. First, Reider-type inequalities are sho…
Secants, Socles and Stability
Aaron Bertram, Brooke Ullery
The projective space of symmetric tensors of degree d can be reinterpreted as a projective space of finite, graded Gorenstein rings with socle in degree d. Via a pair of explicit s…
Le Potier's strange duality, quot schemes, and multiple point formulas for del Pezzo surfaces
Aaron Bertram, Thomas Goller, Drew Johnson
We study Le Potier's strange duality on del Pezzo surfaces using quot schemes to construct independent sections of theta line bundles on moduli spaces of sheaves, one of which is t…
Change of polarization for moduli of sheaves on surfaces as Bridgeland wall-crossing
Aaron Bertram, Cristian Martinez
We prove that the "Thaddeus flips" of -twisted sheaves constructed by Matsuki and Wentworth can be obtained via Bridgeland wall-crossing. Similarly, we realize the change of pol…
The birational geometry of moduli space of sheaves on the projective plane
Aaron Bertram, Cristian Martinez, Jie Wang
We describe a close relation between wall crossings in the birational geometry of moduli space of Gieseker stable sheaves on $\bb{P}^2$ and mini-wall crossings in the stab…
Polynomiality, Wall Crossings and Tropical Geometry of Rational Double Hurwitz Cycles
Aaron Bertram, Renzo Cavalieri, Hannah Markwig
We study rational double Hurwitz cycles, i.e. loci of marked rational stable curves admitting a map to the projective line with assigned ramification profiles over two fixed branch…