000148245 001__ 148245
000148245 005__ 20250115115947.0
000148245 020__ $$a978-3-030-61958-9
000148245 0247_ $$2doi$$a10.1007/978-3-030-61958-9_7
000148245 037__ $$aBOOK-2025-040
000148245 041__ $$aeng
000148245 100__ $$aArtal Bartolo, Enrique $$b
000148245 245__ $$aCremona Transformations of Weighted Projective Planes, Zariski Pairs, and Rational Cuspidal Curves
000148245 250__ $$a1st ed.
000148245 260__ $$aCham$$bSpringer Nature$$c2021
000148245 300__ $$a117–157
000148245 506__ $$aall-rights-reserved
000148245 520__ $$aIn this work, we study a family of Cremona transformations of weighted projective planes which generalize the standard Cremona transformation of the projective plane. Starting from special plane projective curves we construct families of curves in weighted projective planes with special properties. We explain how to compute the fundamental groups of their complements, using the blow-up-down decompositions of the Cremona transformations, we find examples of Zariski pairs in weighted projective planes (distinguished by the Alexander polynomial). As another application of this machinery we study a family of singularities called weighted Lê–Yomdin, which provide infinitely many examples of surface singularities with a rational homology sphere link. To end this paper we also study a family of surface singularities generalizing Brieskorn–Pham singularities in a different direction. This family contains infinitely many examples of integral homology sphere links, answering a question by Némethi.
000148245 540__ $$9info:eu-repo/semantics/closedAccess
000148245 700__ $$aCogolludo-Agustín, José I. $$b
000148245 700__ $$aMartín-Morales, Jorge $$b
000148245 773__ $$tSingularities and Their Interaction with Geometry and Low Dimensional Topology
000148245 8560_ $$fagroca@unizar.es
000148245 8564_ $$s719461$$uhttps://zaguan.unizar.es/record/148245/files/BOOK-2025-040.pdf$$ySin acceso$$zSin acceso
000148245 909CO $$ooai:zaguan.unizar.es:148245$$pbooks
000148245 980__ $$aBOOK$$bCAPITULOS$$b