An official website of the United States government
Abstract We discuss various applications of a uniform vanishing result for the graded components of the finite length Koszul module associated to a subspace$$K\subseteq \bigwedge ^2 V$$ , whereVis a vector space. Previously Koszul modules of finite length have been used to give a proof of Green’s Conjecture on syzygies of generic canonical curves. We now give applications to effective stabilization of cohomology of thickenings of algebraic varieties, divisors on moduli spaces of curves, enumerative geometry of curves onK3 surfaces and to skew-symmetric degeneracy loci. We also show that the instability of sufficiently positive rank 2 vector bundles on curves is governed by resonance and give a splitting criterion.
more »
« less
Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher.
Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?
Some links on this page may take you to non-federal websites. Their policies may differ from this site.
-
-
In this paper we define an interesting family of perfect ideals of codimension three, with five generators, of Cohen-Macaulay type two with trivial multiplication on the $$ \operatorname {Tor}$$ algebra. This family is likely to play a key role in classifying perfect ideals with five generators of type two.more » « less
-
In this paper we give some branching rules for the fundamental representations of Kac--Moody Lie algebras associated to $$T$$-shaped graphs. These formulas are useful to describe generators of the generic rings for free resolutions of length three described in \cite{JWm18}. We also make some conjectures about the generic rings.more » « less
-
We use the Kempf-Lascoux-Weyman geometric technique in order to determine the minimal free resolutions of some orbit closures of quivers. As a consequence, we obtain that for Dynkin quivers orbit closures of 1-step representations are normal with rational singularities. For Dynkin quivers of type $$ \mathbb{A}$$, we describe explicit minimal generators of the defining ideals of orbit closures of 1-step representations. Using this, we provide an algorithm for type $$ \mathbb{A}$$ quivers for describing an efficient set of generators of the defining ideal of the orbit closure of any representation.more » « less
