• Publications
  • Influence
The intrinsic normal cone
Abstract.Let $X$ be an algebraic stack in the sense of Deligne-Mumford. We construct a purely $0$-dimensional algebraic stack over $X$ (in the sense of Artin), the intrinsic normal cone ${\frakExpand
Symmetric Obstruction Theories and Hilbert Schemes of Points on Threefolds
Recall that in an earlier paper by one of the authors DonaldsonThomas type invariants were expressed as certain weighted Euler characteristics of the moduli space. The Euler characteristic isExpand
Orbifold cohomology for global quotients
For an orbifold X which is the quotient of a manifold Y by a finite group G we construct a noncommutative ring with an action of G such that the orbifold cohomology of X as defined in math.AG/0004129Expand
Orbifold techniques in degeneration formulas
We give an approach for relative and degenerate Gromov--Witten invariants, inspired by that of Jun Li but replacing predeformable maps by transversal maps to a twisted target. The main advantage is aExpand
Fundamental Algebraic Geometry
Grothendieck topologies, fibered categories and descent theory: Introduction Preliminary notions Contravariant functors Fibered categories Stacks Construction of Hilbert and Quot schemes:Expand
Smooth toric Deligne-Mumford stacks
Abstract We give a geometric definition of smooth toric Deligne-Mumford stacks using the action of a “torus”. We show that our definition is equivalent to the one of Borisov, Chen and Smith in termsExpand
Orbifold thechniques in degeneration formulas
We give a new approach for relative and degenerate Gromov-Witten invariants, inspired by that ofJun Li but replacing predeformable maps by transversal maps to a twisted target. The main advantageExpand
Stable Maps and Branch Divisors
We construct a natural branch divisor for equidimensional projective morphisms where the domain has lci singularities and the target is nonsingular. The method involves generalizing a divisorExpand
Riemann-Roch theorems and elliptic genus for virtually smooth schemes
For a proper scheme X with a fixed 1‐perfect obstruction theory E , we define virtual versions of holomorphic Euler characteristic, y ‐genus and elliptic genus; they are deformation invariant andExpand
Gerstenhaber and Batalin–Vilkovisky Structures on Lagrangian Intersections
Let M and N be Lagrangian submanifolds of a complex symplectic manifold S. We construct a Gerstenhaber algebra structure on \(\mathcal{T}or_\ast^{\mathcal{O}_S}(\mathcal{O}_M,\mathcal{O}_N)\) and aExpand