2 citations · 3 across the 5 of their papers we have counts for
7 papers
The moduli space of maps from hypersurfaces and its Goodwillie tower
Alexis Aumonier
We define a moduli space of continuous maps from smooth hypersurfaces varying in an ample linear system. To study its topology, we construct a scanning map to an appropriate sectio…
Weiss derivatives of holomorphic maps
Alexis Aumonier
We propose an orthogonal approach to the stable homotopy type of spaces of holomorphic maps to projective space. We study the Weiss towers of the unitary functors of holomorphic an…
Families of algebraic and continuous maps to
Alexis Aumonier
We explain how results comparing the homology of spaces of algebraic and continuous maps to projective spaces can be leveraged to compare moduli stacks of families of algebraic and…
The topology of spaces of holomorphic maps to projective space
Alexis Aumonier
We show that the spaces of holomorphic and continuous maps from a smooth complex projective variety to a projective space have the same homology in a range depending on the degree…
Homological stability for the space of hypersurfaces with marked points
Alexis Aumonier, Ronno Das
We study the space of smooth marked hypersurfaces in a given linear system. Specifically, we prove a homology h-principle to compare it with a space of sections of an appropriate j…
Scanning the moduli of smooth hypersurfaces
Alexis Aumonier
We study the locus of smooth hypersurfaces inside the Hilbert scheme of a smooth projective complex variety. In the spirit of scanning, we construct a map to a continuous section s…
An h-principle for complements of discriminants
Alexis Aumonier
We compare spaces of non-singular algebraic sections of ample vector bundles to spaces of continuous sections of jet bundles. Under some conditions, we provide an isomorphism in ho…