7 papers
Poisson K-stability and the semiclassical Yau--Tian--Donaldson correspondence
Vestislav Apostolov, Brent Pym, Jeffrey Streets
We introduce a notion of K-polystability for compact Kähler holomorphic Poisson manifolds. On the one hand, this notion of stability is well-adapted to constructions of moduli spa…
Bondal's conjecture in dimension five
Stéphane Druel, Jorge Vitório Pereira, Brent Pym +1
Bondal's conjecture in Poisson geometry gives lower bounds on the degeneracy loci of Poisson Fano manifolds, where the rank of the Poisson structure drops. By work of several autho…
Weighted blowups and 3d Poisson desingularizations
Simon Lapointe, Mykola Matviichuk, Brent Pym +1
We establish existence of functorial orbifold reductions of singularities for Poisson subvarieties in smooth Poisson threefolds. Namely, we show that with enough weighted blowups,…
Regularized integrals and manifolds with log corners
Clément Dupont, Erik Panzer, Brent Pym
We introduce a natural geometric framework for the study of logarithmically divergent integrals on manifolds with corners and algebraic varieties, using the techniques of logarithm…
Logarithmic morphisms, tangential basepoints, and little disks
Clément Dupont, Erik Panzer, Brent Pym
We develop the theory of "virtual morphisms" in logarithmic algebraic geometry, introduced by Howell. It allows one to give algebro-geometric meaning to various useful maps of topo…
Creating quantum projective spaces by deforming q-symmetric algebras
Mykola Matviichuk, Brent Pym, Travis Schedler
We construct a large collection of "quantum projective spaces", in the form of Koszul, Calabi-Yau algebras with the Hilbert series of a polynomial ring. We do so by starting with t…