Yalong Cao

Orientability for gauge theories on Calabi–Yau manifolds

Abstract We study orientability issues of moduli spaces from gauge theories on Calabi–Yau manifolds. Our results generalize and strengthen those for Donaldson–Thomas theory on Calabi–Yau manifolds of dimensions 3 and 4. We also prove a corresponding result in the relative situation which is relevant to the gluing formula in DT theory.

Relative Donaldson-Thomas theory for Calabi-Yau 4-folds

Given a complex 4-fold

Zero-dimensional Donaldson–Thomas invariants of Calabi–Yau 4-folds

X

Genus zero Gopakumar–Vafa type invariants for Calabi–Yau 4-folds

with an (Calabi-Yau 3-fold) anti-canonical divisor

Donaldson-Thomas theory for Calabi-Yau 4-folds

Y

Remarks on mirror symmetry of Donaldson-Thomas theory for Calabi-Yau 4-folds

, we study relative Donaldson-Thomas invariants for this pair, which are elements in the Donaldson-Thomas cohomologies of

Counting zero-dimensional subschemes in higher dimensions

Y

Remarks on Kawamata's effective non-vanishing conjecture for manifolds with trivial first Chern classes

. We also discuss gluing formulas which relate relative invariants and

Genus zero Gopakumar-Vafa type invariants for Calabi-Yau 4-folds II: Fano 3-folds

DT_{4}

Counting conics on sextic 4-folds

invariants for Calabi-Yau 4-folds.