# Riemann-Roch Polynomials of the known Hyperk\"ahler Manifolds

@article{Ortiz2020RiemannRochPO, title={Riemann-Roch Polynomials of the known Hyperk\"ahler Manifolds}, author={'Angel David R'ios Ortiz}, journal={arXiv: Algebraic Geometry}, year={2020} }

We compute explicit formulas for the Euler characteristic of line bundles in the two exceptional examples of Hyperkahler Manifolds introduced by O'Grady.

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Positivity of Riemann--Roch polynomials and Todd classes of hyperk\"{a}hler manifolds

- Mathematics
- 2020

For a hyperkahler manifold $X$ of dimension $2n$, Huybrechts showed that there are constants $a_0, a_2, \dots, a_{2n}$ such that $$\chi(L) =\sum_{i=0}^n\frac{a_{2i}}{(2i)!}q_X(c_1(L))^{i}$$ for any… Expand

#### References

SHOWING 1-10 OF 12 REFERENCES

Topological invariants of O’Grady’s six dimensional irreducible symplectic variety

- Mathematics
- 2004

We study O’Grady examples of irreducible symplectic varieties: we establish that both of them can be deformed into lagrangian fibrations. We analyze in detail the topology of the six dimensional… Expand

The Hodge diamond of O’Grady’s six-dimensional example

- Mathematics
- Compositio Mathematica
- 2018

We realize O’Grady’s six-dimensional example of an irreducible holomorphic symplectic (IHS) manifold as a quotient of an IHS manifold of $\text{K3}^{[3]}$ type by a birational involution, thereby… Expand

A finiteness theorem for Lagrangian fibrations

- Mathematics
- 2012

We consider (holomorphic) Lagrangian fibrations X->P^n that satisfy some natural hypotheses. We prove that there are only finitely many such Lagrangian fibrations up to deformation.

Birational geometry of O’Grady’s six dimensional example over the Donaldson–Uhlenbeck compactification

- Mathematics
- 2010

We determine the birational geometry of O’Grady’s six dimensional example over the Donaldson–Uhlenbeck compactification, by looking at the locus of non-locally-free sheaves on the relevant moduli… Expand

Hirzebruch-Riemann-Roch Formulae on Irreducible Symplectic K\

- Mathematics
- 2001

In this article we investigate Hirzebruch-Riemann-Roch formulae for line bundles on irreducible symplectic K\"ahler manifolds. As Huybrechts has shown, for every irreducible complex K\"ahler manifold… Expand

A new six-dimensional irreducible symplectic variety

- Mathematics
- 2000

There are three types of “building blocks” in the Bogomolov decomposition [B, Th.2] of compact Kahlerian manifolds with torsion c1, namely complex tori, CalabiYau varieties, and irreducible… Expand

Desingularized moduli spaces of sheaves on a K3, I

- Mathematics
- 1997

Moduli spaces of semistable torsion-free sheaves on a K3 surface $X$ are often holomorphic symplectic varieties, deformation equivalent to a Hilbert scheme parametrizing zero-dimensional subschemes… Expand

On the Cobordism Class of the Hilbert Scheme of a Surface

- Mathematics
- 1999

Let S be a smooth projective surface and S [n] the Hilbert scheme of zerodimensional subschemes of S of length n. We proof that the class of S [n] in the complex cobordism ring depends only on the… Expand

A hyper-Kähler compactification of the intermediate Jacobian fibration associated with a cubic 4-fold

- Acta Math.,
- 2017