577 research outputs found
Computation of 2-groups of narrow logarithmic divisor classes of number fields
We present an algorithm for computing the 2-group of narrow logarithmic
divisor classes of degree 0 for number fields F. As an application, we compute
in some cases the 2-rank of the wild kernel WK2(F)
Computation of 2-groups of positive classes of exceptional number fields
We present an algorithm for computing the 2-group of the positive divisor
classes of a number field F in case F has exceptional dyadic places. As an
application, we compute the 2-rank of the wild kernel WK2(F) in K2(F) for such
number fields
Towards a Theory of Logarithmic GLSM Moduli Spaces
In this article, we establish foundations for a logarithmic compactification
of general GLSM moduli spaces via the theory of stable log maps. We then
illustrate our method via the key example of Witten's -spin class. In the
subsequent articles, we will push the technique to the general situation. One
novelty of our theory is that such a compactification admits two virtual
cycles, a usual virtual cycle and a "reduced virtual cycle". A key result of
this article is that the reduced virtual cycle in the -spin case equals to
the r-spin virtual cycle as defined using cosection localization by
Chang--Li--Li. The reduced virtual cycle has the advantage of being
-equivariant for a non-trivial -action. The
localization formula has a variety of applications such as computing higher
genus Gromov--Witten invariants of quintic threefolds and the class of the
locus of holomorphic differentials
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