Computations with moduli of perverse point sheaves

Details Computations with moduli of perverse point sheaves Computations with moduli of perverse point sheaves

2003-04-23

arxiv.org/abs/math/0304353v2

Mathematics

Algebraic Geometry

10 pages, sum horrifik tipos correctid

Scientific paper

Given a birational modification $X \to Y$ of complex projective varieties with fiber dimension 1 and rational singularities, consider the main component of Bridgeland's moduli space $W \to Y$ of perverse point sheaves on $X/Y$. We give criteria for the normalization of $W$ to coincide with the transform (flip/flop) $X^+ \to Y$ of $X \to Y$. First, this holds if the exceptional loci of $X \to Y$ and $W \to Y$ have codimension $>1$. Second, if the ideal sheaf of $X \times_Y X^+$ is flat over $X^+$ then there is at least a morphism $X^+ \to W$. We illustrate the results using a number of examples, including surface modifications and standard Francia flips.

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