Zobrazeno 1 - 10
of 65
pro vyhledávání: '"Gillam, W."'
Autor:
Gillam, W. D.
The category of (abstract) fans is to the category of monoids what the category of schemes is to the category of rings: a fan is obtained by gluing spectra of monoids along open embeddings. Here we study the basic algebraic geometry of fans: coherent
Externí odkaz:
http://arxiv.org/abs/1601.02421
Autor:
Gillam, W. D., Karan, A.
In 1914, F. Hausdorff defined a metric on the set of closed subsets of a metric space $X$. This metric induces a topology on the set $H$ of compact subsets of $X$, called the Hausdorff topology. We show that the topological space $H$ represents the f
Externí odkaz:
http://arxiv.org/abs/1601.02425
Autor:
Gillam, W. D.
A map of fine log schemes $X \to Y$ induces a map from the scheme underlying $X$ to Olsson's algebraic stack of strict morphisms of fine log schemes over $Y$. A sheaf on $X$ is called \emph{log flat over} $Y$ iff it is flat over this algebraic stack.
Externí odkaz:
http://arxiv.org/abs/1601.02422
Autor:
Gillam, W. D., Molcho, Sam
We study the category of KM fans - a "stacky" generalization of the category of fans considered in toric geometry - and its various realization functors to "geometric" categories. The "purest" such realization takes the form of a functor from KM fans
Externí odkaz:
http://arxiv.org/abs/1512.07586
Autor:
Gillam, W. D., Molcho, Samouil
We develop a general theory of log spaces, in which one can make sense of the basic notions of logarithmic geometry, in the sense of Fontaine-Illusie-Kato. Many of our general constructions with log spaces are new, even in the algebraic setting. In t
Externí odkaz:
http://arxiv.org/abs/1507.06752
Autor:
Gillam, W. D.
We consider the general problem of deforming a surjective map of modules $f : E \to F$ over a coproduct sheaf of rings $B=B_1 \otimes_A B_2$ when the domain module $E = B_1 \otimes_A E_2$ is obtained via extension of scalars from a $B_2$-module $E_2$
Externí odkaz:
http://arxiv.org/abs/1103.5482
Autor:
Gillam, W. D.
Let $E$ be a rank 2, degree $d$ vector bundle over a genus $g$ curve $C$. The loci of stable pairs on $E$ in class $2[C]$ fixed by the scaling action are expressed as products of $\Quot$ schemes. Using virtual localization, the stable pairs invariant
Externí odkaz:
http://arxiv.org/abs/1103.2169
Autor:
Gillam, W. D.
Given a category fibered in groupoids over schemes with a log structure, one produces a category fibered in groupoids over log schemes. We classify the groupoid fibrations over log schemes that arise in this manner in terms of a categorical notion of
Externí odkaz:
http://arxiv.org/abs/1103.2140
Autor:
Gillam, W. D.
Let $X$ be a ringed space together with the data $M$ of a set $M_x$ of prime ideals of $\O_{X,x}$ for each point $x \in X$. We introduce the localization of $(X,M)$, which is a locally ringed space $Y$ and a map of ringed spaces $Y \to X$ enjoying a
Externí odkaz:
http://arxiv.org/abs/1103.2139
Autor:
Gillam, W. D.
After fixing a non-degenerate bilinear form on a vector space V we define an involution of the manifold of flags F in V by taking a flag to its orthogonal complement. When V is of dimension 3 we check that the Crepant Resolution Conjecture of J. Brya
Externí odkaz:
http://arxiv.org/abs/0708.0842