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Cycle groups for Artin stacks

- A. Kresch
- Mathematics
- 28 October 1998

We construct an algebraic homology functor for Artin stacks of finite type over a field, and we develop intersection-theoretic properties.

Quantum Pieri rules for isotropic Grassmannians

- A. Buch, A. Kresch, Harry Tamvakis
- Mathematics
- 29 September 2008

We study the three point genus zero Gromov-Witten invariants on the Grassmannians which parametrize non-maximal isotropic subspaces in a vector space equipped with a nondegenerate symmetric or… Expand

On the geometry of Deligne-Mumford stacks

- A. Kresch, D. Abramovich, A. Bertram, L. Katzarkov, R. Pandharipande, M. Thaddeus
- Mathematics
- 2009

General structure results about Deligne–Mumford stacks are summarized, applicable to stacks of finite type over a field. When the base field has characteristic 0, a class of “(quasi-)projective”… Expand

Stable Grothendieck polynomials and K-theoretic factor sequences

- A. Buch, A. Kresch, M. Shimozono, Harry Tamvakis, A. Yong
- Mathematics
- 1 December 2005

We formulate a nonrecursive combinatorial rule for the expansion of the stable Grothendieck polynomials of Fomin and Kirillov (Proc Formal Power Series Alg Comb, 1994) in the basis of stable… Expand

Quantum cohomology of the Lagrangian Grassmannian

- A. Kresch, Harry Tamvakis
- Mathematics
- 13 January 2003

Let V be a symplectic vector space and LG be the Lagrangian Grassmannian which parametrizes maximal isotropic subspaces in V. We give a presentation for the (small) quantum cohomology ring QH∗ (LG)… Expand

On Coverings of Deligne–Mumford Stacks and Surjectivity of the Brauer Map

- A. Kresch, Angelo Vistoli
- Mathematics
- 22 January 2003

The paper proves a result on the existence of finite flat scheme covers of Deligne–Mumford stacks. This result is used to prove that a large class of smooth Deligne–Mumford stacks with affine moduli… Expand

Gromov-Witten invariants on Grassmannians

- A. Buch, A. Kresch, Harry Tamvakis
- Mathematics
- 27 June 2003

We prove that any three-point genus zero Gromov-Witten invariant on a type A Grassmannian is equal to a classical intersection number on a two-step flag variety. We also give symplectic and… Expand

Functoriality in intersection theory and a conjecture of Cox

The circuitry is used, for identifying television transmitters, in a television set receiving synchronizing signals and line flyback pulses characteristic of television transmitters, particularly for… Expand

Canonical rational equivalence of intersections of divisors

- A. Kresch
- Mathematics
- 9 October 1997

One way to define an operation in intersection theory is to define a map on the group of algebraic cycles together with a map on the group of rational equivalences which commutes with the boundary… Expand

Quantum cohomology of orthogonal Grassmannians

- A. Kresch, Harry Tamvakis
- Mathematics
- Compositio Mathematica
- 24 June 2003

Let V be a vector space with a non-degenerate symmetric form and OG be the orthogonal Grassmannian which parametrizes maximal isotropic subspaces in V. We give a presentation for the (small) quantum… Expand

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