A Compactification over \overline{𝑀_{𝑔}} of the Universal Moduli Space of Slope-Semistable Vector Bundles

Abstract

Contents 0. Introduction 425 1.The quotient construction 428 2. The fiberwise G.I.T. problem 433 3. Cohomology bounds 435 4. Slope-unstable, torsion free sheaves 437 5. Special, torsion bounded sheaves 440 6. Slope-semistable, torsion free sheaves 443 7. Two results in geometric invariant theory 449 8.The construction of U g (e, r) 454 9