scholarly journals Rational maps from punctual Hilbert schemes of K3 surfaces

2014 ◽  
Vol 146 (3-4) ◽  
pp. 531-538
Author(s):  
Hsueh-Yung Lin
Keyword(s):  
K3 Surfaces ◽  
Rational Maps ◽  
Hilbert Schemes

scholarly journals The standard conjectures for holomorphic symplectic varieties deformation equivalent to Hilbert schemes of K3 surfaces

2013 ◽  
Vol 149 (3) ◽  
pp. 481-494 ◽  
Author(s):  
François Charles ◽  
Eyal Markman
Keyword(s):  
Hilbert Scheme ◽  
K3 Surfaces ◽  
Cohomology Algebra ◽  
Hilbert Schemes ◽  
Projective Varieties ◽  
Hilbert Scheme Of Points ◽  
Complex Projective ◽  
Symplectic Varieties

AbstractWe prove the standard conjectures for complex projective varieties that are deformations of the Hilbert scheme of points on a K3 surface. The proof involves Verbitsky’s theory of hyperholomorphic sheaves and a study of the cohomology algebra of Hilbert schemes of K3 surfaces.

scholarly journals Stability of some vector bundles on Hilbert schemes of points on K3 surfaces

2021 ◽  
Author(s):  
Fabian Reede ◽  
Ziyu Zhang
Keyword(s):  
Moduli Space ◽  
Hilbert Scheme ◽  
Vector Bundles ◽  
K3 Surfaces ◽  
Hilbert Schemes ◽  
Connected Component ◽  
Stable Vector Bundles ◽  
Universal Family ◽  
Hilbert Scheme Of Points ◽  
Flat Family

AbstractLet X be a projective K3 surfaces. In two examples where there exists a fine moduli space M of stable vector bundles on X, isomorphic to a Hilbert scheme of points, we prove that the universal family $${\mathcal {E}}$$ E on $$X\times M$$ X × M can be understood as a complete flat family of stable vector bundles on M parametrized by X, which identifies X with a smooth connected component of some moduli space of stable sheaves on M.

scholarly journals Computing cup products in integral cohomology of Hilbert schemes of points on K3 surfaces

2016 ◽  
Vol 19 (1) ◽  
pp. 78-97
Author(s):  
Simon Kapfer
Keyword(s):  
Computer Program ◽  
Hilbert Scheme ◽  
K3 Surfaces ◽  
K3 Surface ◽  
Hilbert Schemes ◽  
Integral Cohomology ◽  
Cup Products ◽  
By Products

We study cup products in the integral cohomology of the Hilbert scheme of $n$ points on a K3 surface and present a computer program for this purpose. In particular, we deal with the question of which classes can be represented by products of lower degrees.Supplementary materials are available with this article.

scholarly journals Hilbert schemes of points on some K3 surfaces and Gieseker stable bundles

1996 ◽  
Vol 120 (2) ◽  
pp. 255-261 ◽  
Author(s):  
Ugo Bruzzo ◽  
Antony Maciocia
Keyword(s):  
Moduli Spaces ◽  
Wide Class ◽  
Vector Bundles ◽  
K3 Surfaces ◽  
Hilbert Schemes ◽  
Stable Bundles ◽  
Stable Vector Bundles

AbstractBy using a Fourier-Mukai transform for sheaves on K3 surfaces we show that for a wide class of K3 surfaces X the Hilbert schemes Hilbn(X) can be identified for all n ≥ 1 with moduli spaces of Gieseker stable vector bundles on X. We also introduce a new Fourier-Mukai type transform for such surfaces.

scholarly journals Refined Verlinde formulas for Hilbert schemes of points and moduli spaces of sheaves on K3 surfaces

2020 ◽  
Vol Volume 4 ◽  
Author(s):  
Lothar Göttsche
Keyword(s):  
Moduli Spaces ◽  
Generating Functions ◽  
K3 Surfaces ◽  
Line Bundles ◽  
Hilbert Schemes ◽  
Moduli Spaces Of Sheaves ◽  
Elliptic Genera ◽  
Determinant Line Bundles

We compute generating functions for elliptic genera with values in line bundles on Hilbert schemes of points on surfaces. As an application we also compute generating functions for elliptic genera with values in determinant line bundles on moduli spaces of sheaves on K3 surfaces.

scholarly journals Derived equivalent Hilbert schemes of points on K3 surfaces which are not birational

2019 ◽  
Vol 294 (3-4) ◽  
pp. 871-880 ◽  
Author(s):  
Ciaran Meachan ◽  
Giovanni Mongardi ◽  
Kōta Yoshioka
Keyword(s):  
K3 Surfaces ◽  
Hilbert Schemes

scholarly journals Hilbert schemes of K3 surfaces are dense in moduli

2016 ◽  
Vol 290 (5-6) ◽  
pp. 876-884 ◽  
Author(s):  
Eyal Markman ◽  
Sukhendu Mehrotra
Keyword(s):  
K3 Surfaces ◽  
Hilbert Schemes
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