ar X iv : a lg - g eo m / 9 51 10 16 v 1 2 4 N ov 1 99 5 Exceptional and Rigid Sheaves on Surfaces with Anticanonical Class without Base Components .

ar X iv : a lg - g eo m / 9 71 10 29 v 1 2 4 N ov 1 99 7 CLASSIFICATION OF EXCEPTIONAL COMPLEMENTS : ELLIPTIC CURVE CASE

We classify the log del Pezzo surface (S, B) of rank 1 with no 1-,2-,3-,4-, or 6-complements with the additional condition that B has one irreducible component C which is an elliptic curve and C has the coefficient b in B with 1 n ⌊(n + 1)b⌋ = 1 for n=1,2,3,4, and 6.

ar X iv : a lg - g eo m / 9 70 70 16 v 1 2 5 Ju l 1 99 7 RATIONAL CURVES ON QUASI - PROJECTIVE SURFACES

§

ar X iv : a lg - g eo m / 9 71 10 28 v 1 2 1 N ov 1 99 7 On moduli spaces of 4 - or 5 - instanton bundles

We study the scheme of multi-jumping lines of an n-instanton bundle mainly for n ≤ 5. We apply it to prove the irreducibility and smoothness of the moduli space of 5-instanton. Some particular situations with higher c 2 are also studied.

ar X iv : a lg - g eo m / 9 50 20 26 v 2 9 M ay 1 99 5 ALGEBRAIC SURFACES AND SEIBERG - WITTEN INVARIANTS

ar X iv : a lg - g eo m / 9 70 30 04 v 1 5 M ar 1 99 7 Geometry of Moduli Spaces of Flat Bundles on Punctured Surfaces

For a Riemann surface with one puncture we consider moduli spaces of flat connections such that the monodromy transformation around the puncture belongs to a given conjugacy class with the property that a product of its distinct eigenvalues is not equal to 1 unless we take all of them. We prove that these moduli spaces are smooth and their natural closures are normal with rational singularities.