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 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 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 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 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.

scholarly journals Motivic integral of K3 surfaces over a non-archimedean field

2011 ◽  
Vol 228 (5) ◽  
pp. 2688-2730 ◽  
Author(s):  
Allen J. Stewart ◽  
Vadim Vologodsky
Keyword(s):  
K3 Surfaces

scholarly journals Verlinde formulae on complex surfaces: K-theoretic invariants

2021 ◽  
Vol 9 ◽  
Author(s):  
L. Göttsche ◽  
M. Kool ◽  
R. A. Williams
Keyword(s):  
Moduli Space ◽  
K3 Surfaces ◽  
Complex Surfaces ◽  
Type Formula ◽  
Verlinde Formula ◽  
Donaldson Invariants

Abstract We conjecture a Verlinde type formula for the moduli space of Higgs sheaves on a surface with a holomorphic 2-form. The conjecture specializes to a Verlinde formula for the moduli space of sheaves. Our formula interpolates between K-theoretic Donaldson invariants studied by Göttsche and Nakajima-Yoshioka and K-theoretic Vafa-Witten invariants introduced by Thomas and also studied by Göttsche and Kool. We verify our conjectures in many examples (for example, on K3 surfaces).

scholarly journals Curves on K3 surfaces in divisibility 2

2021 ◽  
Vol 9 ◽  
Author(s):  
Younghan Bae ◽  
Tim-Henrik Buelles
Keyword(s):  
Modular Forms ◽  
K3 Surfaces ◽  
Initial Condition ◽  
Smooth Curves ◽  
Holomorphic Anomaly ◽  
Holomorphic Anomaly Equation ◽  
Anomaly Equation ◽  
Degeneration Formula ◽  
The Relationship ◽  
Level 2

Abstract We prove a conjecture of Maulik, Pandharipande and Thomas expressing the Gromov–Witten invariants of K3 surfaces for divisibility 2 curve classes in all genera in terms of weakly holomorphic quasi-modular forms of level 2. Then we establish the holomorphic anomaly equation in divisibility 2 in all genera. Our approach involves a refined boundary induction, relying on the top tautological group of the moduli space of smooth curves, together with a degeneration formula for the reduced virtual fundamental class with imprimitive curve classes. We use double ramification relations with target variety as a new tool to prove the initial condition. The relationship between the holomorphic anomaly equation for higher divisibility and the conjectural multiple cover formula of Oberdieck and Pandharipande is discussed in detail and illustrated with several examples.

scholarly journals Elliptic Fibrations and Kodaira Dimensions of Schreieder’s Varieties

2021 ◽  
Author(s):  
Alice Garbagnati
Keyword(s):  
K3 Surfaces ◽  
Base Change ◽  
Kodaira Dimension ◽  
Elliptic Surface ◽  
Minimal Resolution ◽  
Elliptic Fibrations ◽  
Smooth Model ◽  
Birational Model ◽  
Hodge Numbers ◽  
Rational Elliptic Surface

Abstract We discuss the birational geometry and the Kodaira dimension of certain varieties previously constructed by Schreieder, proving that in any dimension they admit an elliptic fibration and they are not of general type. The $l$-dimensional variety $Y_{(n)}^{(l)}$, which is the quotient of the product of a certain curve $C_{(n)}$ by itself $l$ times by a group $G\simeq \left ({\mathbb{Z}}/n{\mathbb{Z}}\right )^{l-1}$ of automorphisms, was constructed by Schreieder to obtain varieties with prescribed Hodge numbers. If $n=3^c$ Schreieder constructed an explicit smooth birational model of it, and Flapan proved that the Kodaira dimension of this smooth model is 1, if $c>1$; if $l=2$ it is a modular elliptic surface; if $l=3$ it admits a fibration in K3 surfaces. In this paper we generalize these results: without any assumption on $n$ and $l$ we prove that $Y_{(n)}^{(l)}$ admits many elliptic fibrations and its Kodaira dimension is at most 1. Moreover, if $l=2$, its minimal resolution is a modular elliptic surface, obtained by a base change of order $n$ on a specific extremal rational elliptic surface; if $l\geq 3$ it has a birational model that admits a fibration in K3 surfaces and a fibration in $(l-1)$-dimensional varieties of Kodaira dimension at most 0.

Double cover K3 surfaces of Hirzebruch surfaces

2021 ◽  
Vol 21 (2) ◽  
pp. 221-225
Author(s):  
Taro Hayashi
Keyword(s):  
Rational Surface ◽  
K3 Surfaces ◽  
Double Cover ◽  
Double Covering ◽  
Smooth Surfaces ◽  
Branch Locus ◽  
Hirzebruch Surfaces ◽  
Double Covers

Abstract General K3 surfaces obtained as double covers of the n-th Hirzebruch surfaces with n = 0, 1, 4 are not double covers of other smooth surfaces. We give a criterion for such a K3 surface to be a double covering of another smooth rational surface based on the branch locus of double covers and fibre spaces of Hirzebruch surfaces.

Sign in / Sign up

Export Citation Format

Share Document