On topological invariants of algebraic threefolds with (Q-factorial) singularities

• Verfasst von: Grassi, Antonella [VerfasserIn]
• Verfasst von: Weigand, Timo [VerfasserIn]
• Verfasst von: Srinivas, Vasudevan [VerfasserIn]
• Titel: On topological invariants of algebraic threefolds with (Q-factorial) singularities
• Verf.angabe: Antonella Grassi and Timo Weigand
• E-Jahr: 2018
• Jahr: 6 Apr 2018
• Umfang: 37 S.
• Fussnoten: With an appendix [S. 36-37] by V. Srinivas: The @cohomology classes of divisors on somenormal projective complex varieties ; Gesehen am 11.11.2020
• Titel Quelle: Enthalten in: De.arxiv.org
• Ort Quelle: [S.l.] : Arxiv.org, 1991
• Jahr Quelle: 2018
• Band/Heft Quelle: (2018) Artikel-Nummer 1804.02424, 37 Seiten
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: High Energy Physics - Theory
• Sach-SW: Mathematics - Algebraic Geometry
• Sach-SW: Mathematics - Geometric Topology
• K10plus-PPN: 1586178024

Abstract

We study local, global and local-to-global properties of threefolds with certain singularities. We prove criteria for these threefolds to be rational homology manifolds and conditions for threefolds to satisfy rational Poincar\'e duality. We relate the topological Euler characteristic of elliptic Calabi-Yau threefolds with $\mathbb Q$-factorial terminal singularities to dimensions of Lie algebras and certain representations, Milnor and Tyurina numbers and other birational invariants of an elliptic fibration. We give an interpretation in terms of complex deformations. We state a conjecture on the extension of Kodaira's classification of singular fibers on relatively minimal elliptic surfaces to the class of birationally equivalent relatively minimal genus one fibered varieties and we give results in this direction.