In this paper, we propose an ansatz for defining Gopakumar–Vafa invariants of Calabi–Yau
threefolds, using perverse sheaves of vanishing cycles. Our proposal is a modification of a …

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We describe new components of the Gieseker–Maruyama moduli scheme M (n) M (n) of
semistable rank 2 sheaves E on P^ 3 P 3 with c_1 (E)= 0 c 1 (E)= 0, c_2 (E)= nc 2 (E)= n and …

We study admissible subcategories of derived categories of coherent sheaves on del Pezzo
surfaces and rational elliptic surfaces. Using a relation between admissible subcategories …

In this article we provide a stack-theoretic framework to study the universal tropical Jacobian
over the moduli space of tropical curves. We develop two approaches to the process of …

To every singular reduced projective curve X one can associate, following Esteves, many
fine compactified Jacobians, depending on the choice of a polarization on X, each of which …

This paper studies the local geometry of compactified Jacobians. The main result is a
presentation of the completed local ring of the compactified Jacobian of a nodal curve as an …

We study the cohomology of Jacobians and Hilbert schemes of points on reduced and
locally planar curves, which are however allowed to be singular and reducible. We show …

We compute the supports of the perverse cohomology sheaves of the Hitchin fibration for GL
n over the locus of reduced spectral curves. In contrast to the case of meromorphic Higgs …

To every reduced (projective) curve X with planar singularities one can associate, following
E Esteves, many fine compactified Jacobians, depending on the choice of a polarization on …