# Hermite Reciprocity and Schwarzenberger Bundles

@article{Raicu2021HermiteRA, title={Hermite Reciprocity and Schwarzenberger Bundles}, author={Claudiu Raicu and Steven V. Sam}, journal={Commutative Algebra}, year={2021} }

Hermite reciprocity refers to a series of natural isomorphisms involving compositions of symmetric, exterior, and divided powers of the standard SL2-representation. We survey several equivalent constructions of these isomorphisms, as well as their recent applications to Green’s Conjecture on syzygies of canonical curves. The most geometric approach to Hermite reciprocity is based on an idea of Voisin to realize certain multilinear constructions cohomologically by working on a Hilbert scheme of…

## References

SHOWING 1-10 OF 34 REFERENCES

### Universal secant bundles and syzygies of canonical curves

- Mathematics
- 2020

We introduce a relativization of the secant sheaves from Green and Lazarsfeld (A simple proof of Petri’s theorem on canonical curves, Geometry Today, 1984) and Ein and Lazarsfeld (Inventiones Math…

### Singularities and syzygies of secant varieties of nonsingular projective curves

- MathematicsInventiones mathematicae
- 2020

In recent years, the equations defining secant varieties and their syzygies have attracted considerable attention. The purpose of the present paper is to conduct a thorough study on secant varieties…

### Betti numbers of graded modules and cohomology of vector bundles

- Mathematics
- 2007

Mats Boij and Jonas Soederberg (math.AC/0611081) have conjectured that the Betti table of a Cohen-Macaulay module over a polynomial ring can be decomposed in a certain way as a positive linear…

### Straightening Law and Powers of Determinantal Ideals of Hankel Matrices

- Mathematics
- 1998

In this paper we establish a standard monomial theory for generic Hankel matrices. By a generic Hankel matrix we mean a matrix Y=( yij) with yij=x i+ j&1 where the x i are indeterminates over a field…

### Bi-graded Koszul modules, K3 carpets, and Green's conjecture

- MathematicsCompositio Mathematica
- 2022

We extend the theory of Koszul modules to the bi-graded case, and prove a vanishing theorem that allows us to show that the canonical ribbon conjecture of Bayer and Eisenbud holds over a field of…

### green's canonical syzygy conjecture for generic curves of odd genus

- MathematicsCompositio Mathematica
- 2005

we prove in this paper the green conjecture for generic curves of odd genus. that is, we prove the vanishing $k_{k,1}(x,k_x)=0$ for x a generic curve of genus $2k+1$. this completes our previous…

### The gonality conjecture on syzygies of algebraic curves of large degree

- Mathematics
- 2014

We show that a small variant of the methods used by Voisin in her study of canonical curves leads to a surprisingly quick proof of the gonality conjecture of Green and the second author, asserting…

### 3264 and All That: A Second Course in Algebraic Geometry

- Mathematics
- 2016

Introduction 1. Introducing the Chow ring 2. First examples 3. Introduction to Grassmannians and lines in P3 4. Grassmannians in general 5. Chern classes 6. Lines on hypersurfaces 7. Singular…

### Green’s generic syzygy conjecture for curves of even genus lying on a K3 surface

- Mathematics
- 2002

for X a variety and L a line bundle on X. Denoting by Kp,q(X,L) the cohomology at the middle of the sequence above, one sees immediately that the surjectivity of the map μ0 is equivalent to K0,2(C,…