The Chow ring of the stack of cyclic covers of the projective line
In this paper we compute the integral Chow ring of the stack of smooth uniform cyclic covers of the projective line and we give explicit generators.
The cohomology rings of moduli stacks of principal bundles over curves.
The concept of (ν)-equivalence in algebraic deformation theory
The cylinder homomorphism associated to quintic fourfolds
The decomposition and specialization of algebraic families of vector bundles
The deformation relation on the set of Cohen-Macaulay modules on a quotient surface singularity
Let X be a quotient surface singularity, and define as the directed graph of maximal Cohen-Macaulay (MCM) modules with edges corresponding to deformation incidences. We conjecture that the number of connected components of is equal to the order of the divisor class group of X, and when X is a rational double point (RDP), we observe that this follows from a result of A. Ishii. We view this as an enrichment of the McKay correspondence. For a general quotient singularity X, we prove the conjecture...
The deformation theory of representations of fundamental groups of compact Kähler manifolds
The geometry of Calogero-Moser systems
We give a geometric construction of the phase space of the elliptic Calogero-Moser system for arbitrary root systems, as a space of Weyl invariant pairs (bundles, Higgs fields) on the -th power of the elliptic curve, where is the rank of the root system. The Poisson structure and the Hamiltonians of the integrable system are given natural constructions. We also exhibit a curious duality between the spectral varieties for the system associated to a root system, and the Lagrangian varieties for...
The Group of Automorphisms of the Modular Function Field.
The Hodge de Rham theory of relative Malcev completion
The Hodge theory of algebraic maps
The Hyperelliptic Locus with Special Reference to Characteristic Two.
The infinitesimal and generalized Hodge Conjecture for some families of sextic threefolds.
The Intersection Matrix of Brieskorn Singularities.
The irreducible components of moduli spaces of vector bundles on surfaces.
The Kodaira dimension of the moduli space of curves of genus ... 23.
The KSBA compactification for the moduli space of degree two pairs
Inspired by the ideas of the minimal model program, Shepherd-Barron, Kollár, and Alexeev have constructed a geometric compactification for the moduli space of surfaces of log general type. In this paper, we discuss one of the simplest examples that fits into this framework: the case of pairs consisting of a degree two surface and an ample divisor . Specifically, we construct and describe explicitly a geometric compactification for the moduli of degree two pairs. This compactification...
The Lefschetz trace formula for algebraic stacks.
The Lefshetz Vanishing Cycles on a Projective Nonsingular Plane Curve.
The line bundles on moduli stacks of principal bundles on a curve.