19 Citations
Ju l 2 02 1 Cohomology of Differential Forms and Feynman diagrams August 2 , 2021
- 2021
arXiv : On topological invariants of algebraic threefolds with ($\mathbb Q$-factorial) singularities
- Mathematics
- 2018
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…
Cones of special cycles of codimension 2 on orthogonal Shimura varieties
- Mathematics
- 2022
Let X be an orthogonal Shimura variety associated to a unimodular lattice. We investigate the polyhedrality of the cone CX of special cycles of codimension 2 on X. We show that the rays generated by…
Perverse schobers and Orlov equivalences
- Mathematics
- 2022
A perverse schober is a categorification of a perverse sheaf proposed by Kapranov–Schechtman. In this paper, we construct examples of perverse schobers on the Riemann sphere, which categorify the…
The vanishing cohomology of non‐isolated hypersurface singularities
- MathematicsJournal of the London Mathematical Society
- 2022
We employ the perverse vanishing cycles to show that each reduced cohomology group of the Milnor fiber, except the top two, can be computed from the restriction of the vanishing cycle complex to only…
14 72 1 v 2 [ he pth ] 2 5 O ct 2 02 1 Cohomology of Differential Forms and Feynman diagrams October 26 , 2021
- 2021
Alexander modules, Mellin transformation and variations of mixed Hodge structures
- Mathematics
- 2021
To any complex algebraic variety endowed with a morphism to a complex affine torus we associate multivariable cohomological Alexander modules, and define natural mixed Hodge structures on their…
Aspherical manifolds, Mellin transformation and a question of Bobadilla–Kollár
- MathematicsJournal für die reine und angewandte Mathematik
- 2021
Abstract In their paper from 2012, Bobadilla and Kollár studied topological conditions which guarantee that a proper map of complex algebraic varieties is a topological or differentiable fibration.…
Complements to Ample Divisors and Singularities
- MathematicsHandbook of Geometry and Topology of Singularities II
- 2021
Non-abelian Mellin Transformations and Applications
- Mathematics
- 2021
We study non-abelian versions of the Mellin transformations, originally introduced by Gabber-Loeser on complex affine tori. Our main result is a generalization to the non-abelian context and with…