5 papers
A Hopf index for isotropic sections of orthogonal bundles
Martijn Kool, Jeongseok Oh, Jørgen Vold Rennemo +1
The Hopf index equates the multiplicity of a zero of a section of a vector bundle with a winding number. We give eight analogues for isotropic sections of bundles with quadratic fo…
Proof of a magnificent conjecture
M. Kool, J. V. Rennemo
Motivated by super-Yang-Mills theory on a Calabi-Yau 4-fold, Nekrasov and Piazzalunga have assigned weights to -tuples of solid partitions and conjectured a formula for their we…
Fixed point loci of moduli spaces of sheaves on toric varieties
Martijn Kool
Extending work of Klyachko and Perling, we develop a combinatorial description of pure equivariant sheaves of any dimension on an arbitrary nonsingular toric variety . Using geo…
Counting surfaces on Calabi-Yau 4-folds I: Foundations
Younghan Bae, Martijn Kool, Hyeonjun Park
This is the first part in a series of papers on counting surfaces on Calabi-Yau 4-folds. Besides the Hilbert scheme of 2-dimensional subschemes, we introduce \emph{two} types of mo…
A virtual - correspondence for projective surfaces
D. van Bree, A. Gholampour, Y. Jiang +1
For a smooth projective surface satisfying and , we study deformation invariants of the pair . Choosing a Brauer-Severi variet…