Geodesic
Logarithmic differential forms on varieties with singularities
Funkcionalʹnyj analiz i ego priloženiâ, Tome 51 (2017) no. 4, pp. 3-15

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In the article we introduce the notion of logarithmic differential forms with poles along a Cartier divisor given on a variety with singularities, discuss some properties of such forms, and describe highly efficient methods for computing the Poincaré series and generators of modules of logarithmic differential forms in various situations. We also examine several concrete examples by applying these methods to the study of divisors on varieties with singularities of many types, including quasi-homogeneous complete intersections, normal, determinantal, and rigid varieties, and so on.
Keywords: logarithmic differential forms, de Rham lemma, normal varieties, PoincarГ© series, complete intersections, determinantal singularities, rigid singularities.
Mots-clés : fans 
@article{FAA_2017_51_4_a0,
     author = {A. G. Aleksandrov},
     title = {Logarithmic differential forms on varieties with singularities},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {3--15},
     publisher = {mathdoc},
     volume = {51},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2017_51_4_a0/}
}
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A. G. Aleksandrov. Logarithmic differential forms on varieties with singularities. Funkcionalʹnyj analiz i ego priloženiâ, Tome 51 (2017) no. 4, pp. 3-15. http://geodesic.mathdoc.fr/item/FAA_2017_51_4_a0/