Local Structure of Brill-noether Strata in the Moduli Space of Flat Stable Bundles
نویسنده
چکیده
We study the Brill-Noether stratification of the coarse moduli space of locally free stable and flat sheaves of a compact Kähler manifold, proving that these strata have quadratic algebraic singularities.
منابع مشابه
Brill–noether Loci of Stable Rank–two Vector Bundles on a General Curve
In this note we give an easy proof of the existence of generically smooth components of the expected dimension of certain Brill–Noether loci of stable rank 2 vector bundles on a curve with general moduli, with related applications to Hilbert scheme of scrolls.
متن کاملRationality and Poincaré Families for Vector Bundles with Extra Structure on a Curve
Iterated Grassmannian bundles over moduli stacks of vector bundles on a curve are shown to be birational to an affine space times a moduli stack of degree 0 vector bundles, following the method of King and Schofield. Applications include the birational type of some Brill-Noether loci, of moduli schemes for vector bundles with parabolic structure or with level structure and for A. Schmitt’s deco...
متن کاملNon-Abelian Zeta Functions for Elliptic Curves
In this paper, new local and global non-abelian zeta functions for elliptic curves are defined using moduli spaces of semi-stable bundles. To understand them, we also introduce and study certain refined Brill-Noether locus in the moduli spaces. Examples of these new zeta functions and a justification of using only semi-stable bundles are given too. We end this paper with an appendix on the so-c...
متن کاملVector Bundles and Brill–Noether Theory
After a quick review of the Picard variety and Brill–Noether theory, we generalize them to holomorphic rank-two vector bundles of canonical determinant over a compact Riemann surface. We propose several problems of Brill–Noether type for such bundles and announce some of our results concerning the Brill–Noether loci and Fano threefolds. For example, the locus of rank-two bundles of canonical de...
متن کاملBrill-Noether theory on singular curves and vector bundles on K3 surfaces
Let C be a smooth curve. Let W r d be the Brill-Noether locus of line bundles of degree d and with r + 1 independent sections. W r d has a expected dimension ρ(r, d) = g − (r + 1)(g − d + r). If ρ(r, d) > 0 then Fulton and Lazarsfeld have proved that W r d is connected. We prove that this is still true if C is a singular irreducible curve lying on a regular surface S with −KS generated by globa...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008