15,660 research outputs found

### Chern-Simons functions on toric Calabi-Yau threefolds and Donaldson-Thomas theory

In this paper, we give a construction of the global Chern-Simons functions
for toric Calabi-Yau stacks of dimension three using strong exceptional
collections. The moduli spaces of sheaves on such stacks can be identified with
critical loci of these functions. We give two applications of these functions.
First, we prove Joyce's integrality conjecture of generalized DT invariants on
local surfaces. Second, we prove a dimension reduction formula for virtual
motives, which leads to two recursion formulas for motivic Donaldson-Thomas
invariants.Comment: A rewritten versoin. Some references adde

### Classification of free actions on complete intersections of four quadrics

In this paper we classify all free actions of finite groups on Calabi-Yau
complete intersection of 4 quadrics in \PP^7, up to projective equivalence.
We get some examples of smooth Calabi-Yau threefolds with large nonabelian
fundamental groups. We also observe the relation between some of these examples
and moduli of polarized abelian surfaces.Comment: 17 pages, 1 tabl

### Uniformly bounded components of normality

Suppose that $f(z)$ is a transcendental entire function and that the Fatou
set $F(f)\neq\emptyset$. Set $B_1(f):=\sup_{U}\frac{\sup_{z\in
U}\log(|z|+3)}{\inf_{w\in U}\log(|w|+3)}$ and
$B_2(f):=\sup_{U}\frac{\sup_{z\in U}\log\log(|z|+30)}{\inf_{w\in
U}\log(|w|+3)},$ where the supremum $\sup_{U}$ is taken over all components of
$F(f)$. If $B_1(f)<\infty$ or $B_2(f)<\infty$, then we say $F(f)$ is strongly
uniformly bounded or uniformly bounded respectively. In this article, we will
show that, under some conditions, $F(f)$ is (strongly) uniformly bounded.Comment: 17 pages, a revised version, to appear in Mathematical Proceedings
Cambridge Philosophical Societ

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