2011/04/07 by Xiao, Liang
#12H25 (primary) 14F40 32C38 14F10 13N05 #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1104.1224
Let X be a proper smooth algebraic variety over a field k of characteristic zero and let D be a divisor with simple normal crossings. Let M be a vector bundle over X-D equipped with a flat connection with possible irregular singularities along D. We define a cleanliness condition which roughly says that the singularities of the connection are controlled by the singularities at the generic points of D. When this condition is satisfied, we compute explicitly the associated log-characteristic cycle, and relate it to the so-called refined irregularities. As a corollary of a log-variant of Kashiwara-Dubson formula, we obtain the Euler characteristic of the de Rham cohomology of the vector bundle, under a mild technical hypothesis on M.