46 citations · 182 across the 23 of their papers we have counts for
6 papers · 1 filter
Stable pairs and log flips
Aaron Bertram
This paper has two parts. In the first part, we review stable pairs and triples on curves, leading up to Thaddeus' diagram of flips and contractions starting from the blow-up of pr…
An Application of a Log Version of the Kodaira Vanishing Theorem to Embedded Projective Varieties
Aaron Bertram
Given an embedded smooth projective variety Y in CP^n, we show how the existence of a hypersurface with high multiplicity along Y, but of relatively low degree and log canonical ne…
Quantum multiplication of Schur polynomials
Aaron Bertram, Ionut Ciocan-Fontanine, William Fulton
We give formulas for the products of classes of Schubert varieties in the quantum cohomology rings of Grassmannians, in terms of the combinatorics of partitions and tableaux.
Quantum Schubert Calculus
Aaron Bertram
This paper works out the versions of the classical Giambelli and Pieri formulas in the context of quantum cohomology of a complex Grassmannian.
Towards a Schubert calculus for maps from a Riemann surface to a Grassmannian
Aaron Bertram
The intuitive notion of the Gromov invariant for maps from a Riemann surface to a Grassmannian is shown to agree with the definition in \cite{BDW}. Also, an induction on the genus…
Gromov Invariants for Holomorphic Maps from Riemann Surfaces to Grassmannians
Aaron Bertram, Georgios Daskalopoulos, Richard Wentworth
Two compactifications of the space of holomorphic maps of fixed degree from a compact Riemann surface to a Grassmannian are studied. It is shown that the Uhlenbeck compactification…