The Poincaré series of multiplier ideals of a simple complete ideal in a local ring of a smooth surface |
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| Authors: | Carlos Galindo |
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| Institution: | a Departamento de Matemáticas and Instituto Universitario de Matemáticas y Aplicaciones de Castellón (IMAC), Universitat Jaume I, Campus de Riu Sec. s/n, 12071 Castellón, Spain
b Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain |
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| Abstract: | For a simple complete ideal ℘ of a local ring at a closed point on a smooth complex algebraic surface, we introduce an algebraic object, named Poincaré series P℘, that gathers in a unified way the jumping numbers and the dimensions of the vector space quotients given by consecutive multiplier ideals attached to ℘. This paper is devoted to prove that P℘ is a rational function giving an explicit expression for it. |
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| Keywords: | primary 14B05 secondary 13H05 |
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