scholarly journals Higher rank stable pairs on $K3$ surfaces

2012 ◽  
Vol 6 (4) ◽  
pp. 805-847 ◽  
Author(s):  
Benjamin Bakker ◽  
Andrei Jorza
Keyword(s):  
K3 Surfaces ◽  
Higher Rank ◽  
Stable Pairs

scholarly journals Stable pairs on elliptic K3 surfaces

2010 ◽  
Vol 348 (9-10) ◽  
pp. 565-569
Author(s):  
Marcello Bernardara
Keyword(s):  
K3 Surfaces ◽  
Stable Pairs

scholarly journals Stable pairs on local $K3$ surfaces

2012 ◽  
Vol 92 (1) ◽  
pp. 285-370 ◽  
Author(s):  
Yukinobu Toda
Keyword(s):  
K3 Surfaces ◽  
Stable Pairs

scholarly journals HIGHER RANK BRILL–NOETHER THEORY ON SECTIONS OF K3 SURFACES

2012 ◽  
Vol 23 (07) ◽  
pp. 1250075 ◽  
Author(s):  
GAVRIL FARKAS ◽  
ANGELA ORTEGA
Keyword(s):  
Moduli Space ◽  
K3 Surfaces ◽  
Moduli Space Of Curves ◽  
Picard Number ◽  
Detailed Proof ◽  
Rank 2 ◽  
Higher Rank

We discuss the role of K3 surfaces in the context of Mercat's conjecture in higher rank Brill–Noether theory. Using liftings of Koszul classes, we show that Mercat's conjecture in rank 2 fails for any number of sections and for any gonality stratum along a Noether–Lefschetz divisor inside the locus of curves lying on K3 surfaces. Then we show that Mercat's conjecture in rank 3 fails even for curves lying on K3 surfaces with Picard number 1. Finally, we provide a detailed proof of Mercat's conjecture in rank 2 for general curves of genus 11, and describe explicitly the action of the Fourier–Mukai involution on the moduli space of curves.

scholarly journals On the Motivic Stable Pairs Invariants of K3 Surfaces

2016 ◽  
pp. 111-146 ◽  
Author(s):  
S. Katz ◽  
A. Klemm ◽  
R. Pandharipande ◽  
R. P. Thomas
Keyword(s):  
K3 Surfaces ◽  
Stable Pairs

scholarly journals Maps, Sheaves and K3 Surfaces

2017 ◽  
Author(s):  
Rahul Pandharipande
Keyword(s):  
K3 Surfaces ◽  
Stable Maps ◽  
Stable Pairs

The conjectural equivalence of curve counting on Calami- Yau 3-folds via stable maps and stable pairs is discussed. By considering Cali-Yau 3-folds with K3 fibrations, the correspondence naturally connects curve and sheaf counting on K3 surfaces. New conjectures (with D. Maulik) about descendent integration on K3 surfaces are announced. The proof of the complete Yau-Zaslow conjecture is surveyed.

scholarly journals KSBA compactification of the moduli space of K3 surfaces with a purely non-symplectic automorphism of order four

2021 ◽  
Vol 64 (1) ◽  
pp. 99-127
Author(s):  
Han-Bom Moon ◽  
Luca Schaffler
Keyword(s):  
Finite Group ◽  
Moduli Space ◽  
K3 Surfaces ◽  
Double Cover ◽  
Minimal Resolution ◽  
Finite Group Action ◽  
Git Quotient ◽  
Stable Pairs ◽  
A Finite Group ◽  
Order Four

We describe a compactification by KSBA stable pairs of the five-dimensional moduli space of K3 surfaces with a purely non-symplectic automorphism of order four and $U(2)\oplus D_4^{\oplus 2}$ lattice polarization. These K3 surfaces can be realized as the minimal resolution of the double cover of $\mathbb {P}^{1}\times \mathbb {P}^{1}$ branched along a specific $(4,\,4)$ curve. We show that, up to a finite group action, this stable pairs compactification is isomorphic to Kirwan's partial desingularization of the GIT quotient $(\mathbb {P}^{1})^{8}{/\!/}\mathrm {SL}_2$ with the symmetric linearization.

Hyperbolic rigidity of higher rank lattices

2020 ◽  
Vol 53 (2) ◽  
pp. 439-468
Author(s):  
Thomas HAETTEL
Keyword(s):  
Higher Rank
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