Geodesic
On some degeneracy loci in the moduli space of pointed odd spin curves
Algebra i analiz, Tome 32 (2020) no. 5, pp. 1-36.

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $C$ be a smooth projective curve of genus $g\geq 3$ and let $\eta$ be an odd theta characteristic on it such that $h^0(C,\eta) = 1$. Pick a point $p$ from the support of $\eta$ and consider the one-dimensional linear system $|\eta + p|$. In general this linear system is base-point free and all its ramification points are simple. The locus in the moduli space of odd spin curves is studied where the linear system $|\eta + p|$ fails to have this general behavior. This locus is stratified with respect to multiplicities of degeneracies; these strata are called degeneracy schemes and their geometry is explored. Conormal spaces to these schemes are described in intrinsic terms and some consequences of this are presented.
Keywords: moduli spase, projecture curve, theta characteristics, degeneracy scheme. 
@article{AA_2020_32_5_a0,
     author = {M. K. Basok},
     title = {On some degeneracy loci in the moduli space of pointed odd spin curves},
     journal = {Algebra i analiz},
     pages = {1--36},
     publisher = {mathdoc},
     volume = {32},
     number = {5},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AA_2020_32_5_a0/}
}
TY  - JOUR
AU  - M. K. Basok
TI  - On some degeneracy loci in the moduli space of pointed odd spin curves
JO  - Algebra i analiz
PY  - 2020
SP  - 1
EP  - 36
VL  - 32
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AA_2020_32_5_a0/
LA  - en
ID  - AA_2020_32_5_a0
ER  - 
%0 Journal Article
%A M. K. Basok
%T On some degeneracy loci in the moduli space of pointed odd spin curves
%J Algebra i analiz
%D 2020
%P 1-36
%V 32
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AA_2020_32_5_a0/
%G en
%F AA_2020_32_5_a0
M. K. Basok. On some degeneracy loci in the moduli space of pointed odd spin curves. Algebra i analiz, Tome 32 (2020) no. 5, pp. 1-36. http://geodesic.mathdoc.fr/item/AA_2020_32_5_a0/

[1] Atiyah M. F., “Riemann surfaces and spin structures”, Ann. Sci. École Norm. Sup. (4), 4:1 (1971), 47–62 | DOI | MR | Zbl

[2] Bardelli F., “Lectures on stable curves”, Lectures on Riemann Surfaces (Trieste, 1987), World Sci. Publ., Teaneck, NJ, 1989, 648–704 | DOI | MR | Zbl

[3] Cornalba M., “Moduli of curves and theta-characteristics”, Lectures on Riemann surfaces (Trieste, 1987), World Sci. Publ., 1989, 560–589 | DOI | MR | Zbl

[4] Cornalba M., “A remark on the Picard group of spin moduli space”, Atti Accad. Naz. Lincei. Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., 2:3 (1991), 211–217 | MR | Zbl

[5] Eisenbud D., Commutative algebra. With a view toward algebraic geometry, Grad. Texts in Math., 150, Springer-Verlag, New York, 1995 | DOI | MR | Zbl

[6] Arbarello E., Cornalba M., Griffiths Ph., Geometry of algebraic curves, v. II, Grundlehren Math. Wiss., 268, Springer-Verlag, Heidelberg, 2011 | DOI | MR | Zbl

[7] Farkas G., Verra A., “The geometry of the moduli space of odd spin curves”, Ann. of Math. (2), 180:3 (2014), 927–970 | DOI | MR | Zbl

[8] Gamkrelidze R., Lando S., Vassiliev V., Zvonkin A., Graphs on surfaces and their applications, Encyclopaedia Math. Sci., 141, Springer-Verlag, Berlin, 2010 | MR

[9] Harer J., “The rational Picard group of the moduli space of Riemann surfaces with spin structure”, Mapping class groups and moduli spaces of Riemann surfaces, Contemp. Math., 150, Amer. Math. Soc., Gottingen/Seattle, WA, 1991, 1993, 107–136 | DOI | MR | Zbl

[10] Ludwig K., “On the geometry of the moduli space of spin curves”, J. Algebraic Geom., 19:1 (2010), 133–171 | DOI | MR | Zbl

[11] Mumford D., “Theta characteristics of an algebraic curve”, Ann. Sci. École Norm. Sup. (4), 4:2 (1971), 181–192 | DOI | MR | Zbl

[12] Sernesi E., Deformations of algebraic schemes, Grundlehren Math. Wiss., 334, Springer-Verlag, Berlin, 2006 | MR | Zbl