SearcharxivSearch

arXiv · alg-geom/9709002

Wall-crossing formulae for algebraic surfaces with $q>0$

Abstract

We extend the ideas of Friedman and Qin (Flips of moduli spaces and transition formulae for Donaldson polynomial invariants of rational surfaces) to find the wall-crossing formulae for the Donaldson invariants of algebraic surfaces with geometrical genus zero, positive irregularity and anticanonical divisor effective, for any wall $ζ$ with $l_ζ=(ζ\sp{2}-p_1)/4$ being zero or one.

Explore related subjects

Keep this discovery

BibTeXRIS

Vicente Muñoz. 1997-09-04. Wall-crossing formulae for algebraic surfaces with $q>0$. https://arxiv.org/abs/alg-geom/9709002

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Boundedness and $K^2$ for log surfaces

Let $ε, C$ be two positive real numbers, and $\mathcal C \subset \mathbb R$ be a DCC (descending chain condition) set. Let $(X, B = \sum b_j B_j)$ denote a projective surface with an $\mathbb R$-divisor. Then (1) The class $\{X\}$ of surfaces for which there exists a divisor $B$ such that $(X,B)$ is $ε$-log terminal and $-(K_X + B)$ is nef (excluding only those for which at the same time $K_X\equiv 0$, $B=0$, and $X$ has at worst Du Val singularities), is bounded. (2) The set $\{(K_X + B)^2\}$ of squares for the semi log canonical pairs $(X, B)$ with ample $K_X + B$ and $b_j \in \mathcal C$, is a DCC set. (3) The class $\{(X,B)\}$ of pairs such that $(X, B)$ is semi log canonical, $K_X + B$ is ample, $(K_X + B)^2 = C$ and $b_j \in \mathcal C$, is bounded.

alg-geom

Plane Curves with Hyperbolic and C-hyperbolic Complements

The general problem which initiated this work is: What are the quasiprojective varieties which can be uniformized by means of bounded domains in $\cz^n$ ? Such a variety should be, in particular, C--hyperbolic, i.e. it should have a Carathéodory hyperbolic covering. We study here the plane projective curves whose complements are C--hyperbolic. For instance, we show that most of the curves whose duals are nodal or, more generally, immersed curves, belong to this class. We also give explicit examples of irreducible such curves of any even degree d greater or equal 6.

alg-geom