Resolution of singularities of the cotangent sheaf of a singular variety
Freitag, 9.2.18, 10:30-11:30, Hörsaal FRIAS, Albertsstr. 19
The subject of the talk is resolution of singularities of differential forms on an algebraic or analytic variety. We address the problem of finding a resolution of singularities \(\bsigma : X \bto X_0 \) of a singular algebraic or analytic variety \(X_0\) such that the pulled back cotangent sheaf of \(X_0\) (i.e., the pull-back of the Kahler differential forms defined in \(X_0\)) is given, locally in \(X\), by monomial differential forms (with respect to a suitable coordinate system). This problem is related with monomialization of maps, the \(L^2\) cohomology of singular varieties and reduction of singularities of vector-fields. In a work in collaboration with Bierstone, Grandjean and Milman, we give a positive answer to the problem when \(dim\b, X_0 \bleq 3\).
On the topology of smooth hypersurfaces
Freitag, 9.2.18, 10:30-11:30, Hörsaal FRIAS, Albertstr. 19
To what extent the Chern class of a divisor (in singular\ncohomology) determines its topology?\nDiscussion of a conjecture by Totaro concerning the topology\nof smooth hypersurfaces on projective manifolds.
Algebraic curves and modular forms of low degree
Freitag, 23.2.18, 10:30-11:30, Hörsaal FRIAS, Albertstr. 19
For genus 2 and 3 modular forms are intimately connected with\nthe moduli of curves of genus 2 and 3. We give an explicit way to\ndescribe such modular forms for genus 2 and 3\nusing invariant theory and give some applications.\nThis is based on joint work with Fabien Clery and Carel Faber.\n