Explore: Vector Bundles On Curves And Their Moduli

University Press. "Algebraic Stacks and Moduli of Vector Bundles" (PDF). Moduli theory Moduli stacks in P-adic modular forms and Langlands program Grothendieck

line bundles to higher rank. This idea would prove fruitful, in terms of moduli spaces of vector bundles. following on the work in the 1960s on geometric

motivations for analyzing stable vector bundles is their nice behavior in families. In fact, Moduli spaces of stable vector bundles can be constructed using the

considered while constructing the Hilbert scheme of curves (and the moduli space of algebraic curves). This polynomial is H C ( t ) = ( 6 t − 1 ) ( g −

MR 3887650 C. Sorger, Lectures on moduli of principal G-bundles over algebraic curves Geometric Langlands conjectures Ran space Moduli stack of vector bundles

Several properties of ample line bundles extend to ample vector bundles. For example, a vector bundle F is ample if and only if high symmetric powers of

is the moduli stack of line bundles with n {\displaystyle n} -sections. This follows directly from the definition of quotient stacks evaluated on points

Hoffman, Norbert (2010). "Moduli Stacks of Vector Bundles on Curves and the King–Schofield Rationality Proof". Cohomological and Geometric Approaches to

theory, and so their study is of considerable interest in physics. The apparatus of vector bundles, principal bundles, and connections on bundles plays

possibility: the cone of curves may be spanned by one (−2)-curve and one curve with self-intersection 0.) So the cone of curves is either the standard round