Donaldson Thomas invariant of P^1 scroll

Details Donaldson Thomas invariant of P^1 scroll Donaldson Thomas invariant of P^1 scroll

2007-11-28

arxiv.org/abs/0711.4529v3

Mathematics

Algebraic Geometry

Scientific paper

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.

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