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Universal covering spaces and fundamental groups in algebraic geometry as schemes
algebraic geometry fundamental groups
2015/7/14
In topology, the notions of the fundamental group
and the universal cover are closely intertwined. By importing
usual notions from topology into the algebraic and arithmetic setting, we construct a ...
MURPHY’S LAW IN ALGEBRAIC GEOMETRY: BADLY-BEHAVED DEFORMATION SPACES
LAW IN ALGEBRAIC GEOMETRY DEFORMATION SPACES
2015/7/14
We consider the question: “How bad can the deformation space of an object
be?” The answer seems to be: “Unless there is some a priori reason otherwise, the deformation space may be as bad as possible...
Flatness in non-Archimedean analytic geometry
Flatness non-Archimedean analytic geometry Algebraic Geometry
2011/9/16
Abstract: This text is devoted to the systematic study of flatness in the context of Berkovich analytic spaces. After having shown through a counter-example that naive flatness in that context is not ...
A Fourier-Mukai Approach to the Enumerative Geometry of Principally Polarized Abelian Surfaces
ideal sheaf Fourier-Mukai divisor abelian surface Hilbert scheme stable sheaf
2011/9/5
Abstract: We study twisted ideal sheaves of small length on an irreducible principally polarized abelian surface (T,l). Using Fourier-Mukai techniques we associate certain jumping schemes to such shea...
Construction of schemes over $F_1$, and over idempotent rings: towards tropical geometry
$F_1$ over idempotent rings towards tropical geometry
2010/11/26
In this paper, we give some categorical description of the general spectrum functor, defining it as an adjoint of a global section functor.The general spectrum functor includes that of F1 and of semir...
2-plectic geometry, Courant algebroids, and categorified prequantization
2-plectic geometry Courant algebroids categorified prequantization
2010/12/7
A 2-plectic manifold is a manifold equipped with a closed nondegenerate 3-form, just as a symplectic manifold is equipped with a closed nondegenerate 2-form. In 2-plectic geometry we meet higher analo...
Approximations and Lipschitz continuity in p-adic semi-algebraic and subanalytic geometry
Approximations Lipschitz continuity p-adic semi-algebraic subanalytic geometry
2010/12/8
It was already known that a p-adic, locally Lipschitz continuous semialgebraic function is piecewise Lipschitz continuous, where the pieces can be taken semi-algebraic.
In this paper, we develop the theory of flashes of an algebraic curve. We show that the theory is birationally invariant in a sense which we will make more precise below. We also show how the theory p...