scholarly journals Brill–Noether loci in codimension two

2013 ◽  
Vol 149 (9) ◽  
pp. 1535-1568 ◽  
Author(s):  
Nicola Tarasca
Keyword(s):  
Moduli Space ◽  
Moduli Space Of Curves ◽  
Stable Curves ◽  
Codimension Two

AbstractLet us consider the locus in the moduli space of curves of genus$2k$defined by curves with a pencil of degree$k$. Since the Brill–Noether number is equal to$- 2$, such a locus has codimension two. Using the method of test surfaces, we compute the class of its closure in the moduli space of stable curves.

Birational models of 𝓜2,2 arising as moduli of curves with nonspecial divisors

2021 ◽  
Vol 21 (1) ◽  
pp. 23-43
Author(s):  
Drew Johnson ◽  
Alexander Polishchuk
Keyword(s):  
Moduli Space ◽  
Moduli Of Curves ◽  
Moduli Space Of Curves ◽  
Stable Curves ◽  
Moduli Stack

Abstract We study birational projective models of 𝓜2,2 obtained from the moduli space of curves with nonspecial divisors. We describe geometrically which singular curves appear in these models and show that one of them is obtained by blowing down the Weierstrass divisor in the moduli stack of 𝓩-stable curves 𝓜 2,2(𝓩) defined by Smyth. As a corollary, we prove projectivity of the coarse moduli space M 2,2(𝓩).

THE ℚ-PICARD GROUP OF THE MODULI SPACE OF CURVES IN POSITIVE CHARACTERISTIC

2001 ◽  
Vol 12 (05) ◽  
pp. 519-534 ◽  
Author(s):  
ATSUSHI MORIWAKI
Keyword(s):  
Moduli Space ◽  
Cohomology Group ◽  
Positive Characteristic ◽  
Picard Group ◽  
Closed Field ◽  
Moduli Space Of Curves ◽  
Algebraically Closed Field ◽  
Stable Curves ◽  
Étale Cohomology ◽  
Cycle Map

In this note, we prove that the ℚ-Picard group of the moduli space of n-pointed stable curves of genus g over an algebraically closed field is generated by the tautological classes. We also prove that the cycle map to the second étale cohomology group is bijective.

scholarly journals Enumerating Hassett’s Wall and Chamber Decomposition of the Moduli Space of Weighted Stable Curves

2018 ◽  
Vol 29 (1) ◽  
pp. 36-53
Author(s):  
Kenneth Ascher ◽  
Connor Dubé ◽  
Daniel Gershenson ◽  
Elaine Hou
Keyword(s):  
Moduli Space ◽  
Stable Curves

scholarly journals Normal functions and the height of Gross-Schoen cycles

2014 ◽  
Vol 214 ◽  
pp. 53-77 ◽  
Author(s):  
Robin De Jong
Keyword(s):  
Line Bundle ◽  
Moduli Space ◽  
The Self ◽  
Compact Type ◽  
Stable Curves ◽  
Normal Functions ◽  
Chern Form ◽  
Bloch Line ◽  
Pointed Curve ◽  
Dualizing Sheaf

AbstractWe prove a variant of a formula due to Zhang relating the Beilinson– Bloch height of the Gross–Schoen cycle on a pointed curve with the self-intersection of its relative dualizing sheaf. In our approach, the height of the Gross–Schoen cycle occurs as the degree of a suitable Bloch line bundle. We show that the Chern form of this line bundle is nonnegative, and we calculate its class in the Picard group of the moduli space of pointed stable curves of compact type. The basic tools are normal functions and biextensions associated to the cohomology of the universal Jacobian.

Sign in / Sign up

Export Citation Format

Share Document