Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Seshadri constants of varieties with large fundamental group   Let $X$ be a smooth variety and let $L$ be an ample line bundle on $X$. If
$\pi^{alg}_{1}(X)$ is large, we show that the Seshadri constant
$\epsilon(p^{*}L)$ can be made arbitrarily large by passing to a finite \'etale
cover $p:X'\rightarrow X$. This result answers affirmatively a conjecture of
J.-M. Hwang. Moreover, we prove an analogous result when $\pi_{1}(X)$ is large
and residually finite. Finally, under the same topological assumptions, we
appropriately generalize these results to the case of big and nef line bundles.
More precisely, given a big and nef line bundle $L$ on $X$ and a positive
number $N>0$, we show that there exists a finite \'etale cover $p:
X'\rightarrow X$ such that the Seshadri constant $\epsilon(p^{*}L; x)\geq N$
for any $x\notin p^{*}\textbf{B}_{+}(L)=\textbf{B}_{+}(p^{*}L)$, where
$\textbf{B}_{+}(L)$ is the augmented base locus of $L$.

18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys