Mihai Fulger

Positive cones of dual cycle classes

We study generalizations for higher codimension cycles of several well-known definitions of the nef cone of divisors on a projective variety. These generalizations fix some of the pathologies exhibited by the classical nef cone of higher codimension classes. As an application, we recover the expected properties of the pseudoeffective cones

Kernels of numerical pushforwards

\overline{Eff}_{k}(X)

Morphisms and faces of pseudo-effective cones

for all k.

Newton–Okounkov bodies and complexity functions

Abstract Let π : X → Y be a morphism of projective varieties and π∗ :Nk(X) → Nk(Y) the pushforward map of numerical cycle classes. We show that when the Chow groups of points of the fibers are as simple as they can be, then the kernel of π∗ is spanned by k-cycles contracted by π.

Zariski decompositions of numerical cycle classes

Let

The cones of effective cycles on projective bundles over curves

\pi: X \to Y

Volume and Hilbert functions of R-divisors

be a morphism of projective varieties and suppose that

Local volumes on normal algebraic varieties

\alpha

Schur asymptotics of Veronese syzygies

is a pseudo-effective numerical cycle class satisfying

Some splitting criteria on Hirzebruch surfaces

\pi_*\alpha = 0