zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Relative Bogomolov’s inequality and the cone of positive divisors on the moduli space of stable curves. (English) Zbl 0893.14004
Summary: Let f:XY be a surjective and projective morphism of smooth quasi-projective varieties over an algebraically closed field of characteristic zero with dimf=1. Let E be a vector bundle of rank r on X. In this paper, we would like to show that if X y is smooth and E y is semistable for some yY, then f * 2rc 2 (E)-(r-1)c 1 (E) 2 is weakly positive at y. We apply this result to obtain the following description of the cone of weakly positive -Cartier divisors on the moduli space of stable curves. Let ¯ g (resp. g ) be the moduli space of stable (resp. smooth) curves of genus g2. Let λ be the Hodge class, and let the δ i ’s (i=0,...,[g/2]) be the boundary classes. Then, a -Cartier divisor xλ+ i=0 [g/2] y i δ i on ¯ g is weakly positive over g if and only if x0, gx+(8g+4)y 0 0, and i(g-i)x+(2g+1)y i 0 for all 1i[g/2].

MSC:
14H10Families, algebraic moduli (curves)
14C20Divisors, linear systems, invertible sheaves
14G40Arithmetic varieties and schemes; Arakelov theory; heights
57R20Characteristic classes and numbers (differential topology)