02912nam 22005175 450 991074608740332120251008152003.03-031-32115-410.1007/978-3-031-32115-3(MiAaPQ)EBC30745203(Au-PeEL)EBL30745203(DE-He213)978-3-031-32115-3(PPN)27273537X(CKB)28225229100041(EXLCZ)992822522910004120230914d2023 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierNew Techniques in Resolution of Singularities /by Dan Abramovich, Anne Frühbis-Krüger, Michael Temkin, Jarosław Włodarczyk1st ed. 2023.Cham :Springer International Publishing :Imprint: Birkhäuser,2023.1 online resource (345 pages)Oberwolfach Seminars,2296-5041 ;50Print version: Abramovich, Dan New Techniques in Resolution of Singularities Cham : Springer International Publishing AG,c2023 9783031321146 A Computational View on Hironaka’s Resolution of Singularities -- Stacks for Everyone Who Cares About Varieties and Singularities -- Introduction to Logarithmic Geometry -- Birational Geometry Using Weighted Blowing Up -- Relative and Logarithmic Resolution of Singularities -- Weighted Resolution of Singularities. A Rees Algebra Approach -- New Techniques in Resolution of Singularities: Open Problems.Resolution of singularities is notorious as a difficult topic within algebraic geometry. Recent work, aiming at resolution of families and semistable reduction, infused the subject with logarithmic geometry and algebraic stacks, two techniques essential for the current theory of moduli spaces. As a byproduct a short, a simple and efficient functorial resolution procedure in characteristic 0 using just algebraic stacks was produced. The goals of the book, the result of an Oberwolfach Seminar, are to introduce readers to explicit techniques of resolution of singularities with access to computer implementations, introduce readers to the theories of algebraic stacks and logarithmic structures, and to resolution in families and semistable reduction methods.Oberwolfach Seminars,2296-5041 ;50Geometry, AlgebraicAlgebraic GeometryGeometry, Algebraic.Algebraic Geometry.516.35Abramovich Dan472525ühbis-Krüger Anne1428000Temkin Michael1428001Włodarczyk Jarosław1428002MiAaPQMiAaPQMiAaPQBOOK9910746087403321New Techniques in Resolution of Singularities3563105UNINA