On Quasi-Étale Quotients of a Product of Two Curves

2015 ◽  
pp. 149-170 ◽  
Author(s):  
Roberto Pignatelli
Keyword(s):  
Étale Quotients

scholarly journals Moduli of Bridgeland semistable objects on 3-folds and Donaldson–Thomas invariants

2019 ◽  
Vol 2019 (747) ◽  
pp. 175-219 ◽  
Author(s):  
Dulip Piyaratne ◽  
Yukinobu Toda
Keyword(s):  
Finite Type ◽  
Equivalent Form ◽  
Stability Conditions ◽  
Weak Stability ◽  
Algebraic Stacks ◽  
Moduli Stacks ◽  
Étale Quotients

Abstract In this paper we show that the moduli stacks of Bridgeland semistable objects on smooth projective 3-folds are quasi-proper algebraic stacks of finite type if they satisfy the Bogomolov–Gieseker (BG for short) inequality conjecture proposed by Bayer, Macrì and the second author. The key ingredients are the equivalent form of the BG inequality conjecture and its generalization to arbitrary very weak stability conditions. This result is applied to define Donaldson–Thomas invariants counting Bridgeland semistable objects on smooth projective Calabi–Yau 3-folds satisfying the BG inequality conjecture, for example on étale quotients of abelian 3-folds.

scholarly journals MIXED QUASI-ÉTALE QUOTIENTS WITH ARBITRARY SINGULARITIES

2014 ◽  
Vol 57 (1) ◽  
pp. 143-165 ◽  
Author(s):  
DAVIDE FRAPPORTI ◽  
ROBERTO PIGNATELLI
Keyword(s):  
Minimal Surface ◽  
Finite Subset ◽  
General Type ◽  
Minimal Resolution ◽  
Surfaces Of General Type ◽  
Geometric Genus ◽  
Canonical Class ◽  
Two Factors ◽  
Surface Of General Type ◽  
Étale Quotients

AbstractA mixed quasi-étale quotient is the quotient of the product of a curve of genus at least 2 with itself by the action of a group which exchanges the two factors and acts freely outside a finite subset. A mixed quasi-étale surface is the minimal resolution of its singularities. We produce an algorithm computing all mixed quasi-étale surfaces with given geometric genus, irregularity and self-intersection of the canonical class. We prove that all irregular mixed quasi-étale surfaces of general type are minimal. As an application, we classify all irregular mixed quasi-étale surfaces of general type with genus equal to the irregularity, and all the regular ones with K2 > 0, thus constructing new examples of surfaces of general type with χ = 1. We mention the first example of a minimal surface of general type with pg = q = 1 and Albanese fibre of genus bigger than K2.

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