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Donaldson–Thomas invariants for complexes on abelian threefolds

- Martin G. Gulbrandsen
- Mathematics
- 3 November 2011

Donaldson–Thomas invariants for moduli spaces M of perfect complexes on an abelian threefold X are usually zero. A better object is the quotient $${K=[M/X\times\widehat{X}]}$$ of complexes modulo… Expand

Computing the Euler characteristic of generalized Kummer varieties

- Martin G. Gulbrandsen
- Mathematics
- 13 February 2007

We give an elementary proof of the formula χ(KnA)=n3σ(n) for the Euler characteristic of the generalized Kummer variety KnA, where σ(n) denotes the sum of divisors function.

Early recognition of regional cardiac ischemia using a 3-axis accelerometer sensor.

- O. J. Elle, S. Halvorsen, +5 authors E. Fosse
- Medicine
- Physiological measurement
- 15 April 2005

TLDR

A relative Hilbert–Mumford criterion

- Martin G. Gulbrandsen, L. H. Halle, K. Hulek
- Mathematics
- 29 April 2014

We generalize the classical Hilbert–Mumford criteria for GIT (semi-)stability in terms of one parameter subgroups of a linearly reductive group G over a field k, to the relative situation of an… Expand

A GIT construction of degenerations of Hilbert schemes of points

- Martin G. Gulbrandsen, L. H. Halle, K. Hulek
- Mathematics
- 1 April 2016

We present a Geometric Invariant Theory (GIT) construction which allows us to construct good projective degenerations of Hilbert schemes of points for simple degenerations. A comparison with the… Expand

The Euler charateristic of the generalized Kummer scheme of an Abelian threefold

- Martin G. Gulbrandsen, Andrea T. Ricolfi
- Mathematics
- 3 June 2015

Let X be an Abelian threefold. We prove a formula, conjectured by the first author, expressing the Euler characteristic of the generalized Kummer schemes $$K^nX$$KnX of X in terms of the number of… Expand

The geometry of degenerations of Hilbert schemes of points

- Martin G. Gulbrandsen, L. H. Halle, K. Hulek, Ziyu Zhang
- Mathematics
- 2 February 2018

Given a strict simple degeneration $f \colon X\to C$ the first three authors previously constructed a degeneration $I^n_{X/C} \to C$ of the relative degree $n$ Hilbert scheme of $0$-dimensional… Expand

Vector Bundles and Monads On Abelian Threefolds

- Martin G. Gulbrandsen
- Mathematics
- 21 July 2009

The purpose of this article is to construct examples of stable rank 2 vector bundles on abelian threefolds and to study their moduli. More precisely, we consider principally polarized abelian… Expand

Fourier Mukai transforms of line bundles on derived equivalent abelian varieties

- Martin G. Gulbrandsen
- Mathematics
- 14 November 2007

We study the Fourier-Mukai functor D(Y) → D(X) induced by the universal family on a ﬁne moduli space Y for simple semihomogeneous vector bundles on an abelian variety X. The main result is that the… Expand

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