6 papers · 1 filter
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,…
Numerically flat foliations and holomorphic Poisson geometry
Stéphane Druel, Jorge Vitório Pereira, Brent Pym +1
We investigate the structure of smooth holomorphic foliations with numerically flat tangent bundles on compact Kähler manifolds. Extending earlier results on non-uniruled projectiv…
Semiclassical Hodge theory for log Poisson manifolds
Aidan Lindberg, Brent Pym
We construct a mixed Hodge structure on the topological K-theory of smooth Poisson varieties, depending weakly on a choice of compactification. We establish a package of tools for…
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…
Holonomic Poisson manifolds and deformations of elliptic algebras
Brent Pym, Travis Schedler
We introduce a natural nondegeneracy condition for Poisson structures, called holonomicity, which is closely related to the notion of a log symplectic form. Holonomic Poisson manif…