9 papers · 1 filter
Supercycles, stable supermaps and SUSY Nori motives
Ugo Bruzzo, Daniel Hernandez Ruiperez, Yuri I. Manin
We define stable supercurves and stable supermaps, and based on these notions we develop a theory of Nori motives for the category of stable supermaps of SUSY curves with punctures…
Moduli of stable supermaps
Ugo Bruzzo, Daniel Hernández Ruipérez
We review the notion of stable supermap from SUSY curves to a fixed target superscheme, and prove that when the target is (super)projective, stable supermaps are parameterized by a…
An asymptotic description of the Noether-Lefschetz components in toric varieties
Ugo Bruzzo, William D. Montoya
We extend the definition of Noether-Leschetz components to quasi-smooth hypersurfaces in a projective simplicial toric variety of dimension 2k+1, and prove that asymptotically the…
Foundations of superstack theory
Ugo Bruzzo, Daniel Hernández Ruipérez
In view of applications to the construction of moduli spaces of objects in algebraic supergeometry, we start a systematic study of stacks in that context. After defining a supersta…
On the exceptional set of crepant resolutions of abelian singularities
Ugo Bruzzo, Fábio Arceu Ferreira
Let G be a finite abelian subgroup of SL(n,C), and suppose there exists a toric crepant resolution phi: X -- > C^n/G. We prove that for each component E of the exceptional set of p…
Notes on fundamental algebraic supergeometry. Hilbert and Picard superschemes
Ugo Bruzzo, Daniel Hernandez Ruiperez, Alexander Polishchuk
These notes aim at providing a complete and systematic account of some foundational aspects of algebraic supergeometry, namely, the extension to the geometry of superschemes of man…