Donaldson Thomas invariant of P^1 scroll

Abstract

Let X be a P^1 scroll (a compactification of a line bundle L) over a complex surafce S and assume S has a global two form with zero loci a smooth curve C. The Donaldson Thomas invariants of X is shown to be zero if the curve class has is component on S not a multiple of [C]. For nonzero case, when the prime field insertion are above C, the invariant is shown to depend only on the analytic neighborhood of L in X.

References in corpus (2)

• Zero dimensional Donaldson-Thomas invariants of threefolds
• Gromov-Witten invariants of varieties with holomorphic 2-forms