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The intrinsic normal cone

- K. Behrend, B. Fantechi
- Mathematics
- 15 January 1996

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
${\frak… Expand

Symmetric Obstruction Theories and Hilbert Schemes of Points on Threefolds

- K. Behrend, B. Fantechi
- Mathematics
- 24 December 2005

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 is… Expand

Orbifold cohomology for global quotients

- B. Fantechi, L. Goettsche
- Mathematics
- 23 April 2001

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/0004129… Expand

Orbifold techniques in degeneration formulas

- D. Abramovich, B. Fantechi
- Mathematics
- 26 March 2011

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 a… Expand

Fundamental Algebraic Geometry

- B. Fantechi
- Mathematics
- 2005

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

- B. Fantechi, Étienne Mann, F. Nironi
- Mathematics
- 2010

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 terms… Expand

Orbifold thechniques in degeneration formulas

- D. Abramovich, B. Fantechi
- Mathematics
- 28 June 2016

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 advantage… Expand

Stable Maps and Branch Divisors

- B. Fantechi, R. Pandharipande
- Mathematics
- Compositio Mathematica
- 18 May 1999

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 divisor… Expand

Riemann-Roch theorems and elliptic genus for virtually smooth schemes

- B. Fantechi, L. Gottsche
- Mathematics
- 7 June 2007

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 and… Expand

Gerstenhaber and Batalin–Vilkovisky Structures on Lagrangian Intersections

- K. Behrend, B. Fantechi
- Physics
- 2009

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 a… Expand

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