Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bergman kernels and the pseudoeffectivity of relative canonical bundles   The main result of the present article is a (practically optimal) criterium
for the pseudoeffectivity of the twisted relative canonical bundles of
surjective projective maps. Our theorem has several applications in algebraic
geometry; to start with, we obtain the natural analytic generalization of some
semipositivity results due to E. Viehweg and F. Campana. As a byproduct, we
give a simple and direct proof of a recent result due to
  C. Hacon--J. McKernan, S. Takayama and H. Tsuji concerning the extension of
twisted pluricanonical forms. More applications will be offered in the sequel
of this article.

11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat