In particular, this improves upon the results of (Han and Park in Math Ann 375(3–4), 1745–1760, 2019) regarding the arithmetic invariant of the moduli stack ({mathcal {L}}_{1,12n} :=mathrm {Hom}_{n}({mathbb {P}}^1, overline{{mathcal {M}}}_{1,1})) of stable elliptic ...
We define and study the stack {\\mathcal U}^{ns,a}_{g,g} {\\mathcal U}^{ns,a}_{g,g} of (possibly singular) projective curves of arithmetic genus g with g smooth marked points forming an ample non-special divisor. We define an explicit closed embedding of a natural {\\mathbb ...
moduliwittentwistedgaugedstackcurves a r X i v : m a t h / 0 2 1 2 3 1 6 v 1 [ m a t h . A G ] 2 3 D e c 2 0 0 2 November2002math.AG/0212316 OnA-twistedmodulistackforcurvesfrom Witten’sgaugedlinearsigmamodels Chien-HaoLiu 1 DepartmentofMathematics HarvardUniversity Cambri...
Let $E$ be a vector bundle of rank $r\\geq 2$ on a smooth projective curve $C$ of genus $g \\geq 2$ over an algebraically closed field $K$ of arbitrary characteristic. For any integer with $1\\le k\\le r-1$ we define $${\\se}_k(E):=k\\deg E-r\\max\\deg F.$$...
2023-12-20 Mumford's formula on the universal Picard stack 01:13:23 2023-12-14 Log intersection theory of the moduli space of curves 01:27:11 2023-12-12 Physical approach to K-theoretic Donaldson invariants 01:20:51 2023-12-01 Toward a generalization of the Witten conjecture from sp...
The proof is based on a local deformation-theoretic analysis of the map from the stack of pairs (S, X) to the moduli stack of curves g that associates to X the isomorphism class [C] of its normalization.doi:10.1080/00927870802174082
The moduli space M(m) defined above is the moduli stack of elliptic curves with a level m structure [19, section 4.2]. The idea is that Γ(m) preserves the level m structure. To gain a bit of intuition, note that for m=2, Γ(2) preserves a choice of spin structure on T2. If...
A large part of this note describes the algebraic fundamental groups in a concrete manner. This note gives only a sketch of the fundamental groups of the algebraic stack of moduli of curves. Some application to a purely topological statement, i.e., an obstruction to the surjectivity of ...
摘要: We prove that the coarse moduli space of curves of genus six is birational to an arithmetic quotient of a bounded symmetric domain of type IV by giving a period map to the moduli space of some lattice-polarized K3 surfaces.DOI: 10.1090/S0002-9947-2010-05126-8 被引量: 10 ...
We effectively answer the geometric Shafarevich's conjecture on the squarefree odd hyperelliptic curves with a marked Weierstrass point as a consequence of acquiring a family of new sharp asymptotic with the leading term of order $\mathcal{O}\left( \mathcal{B}^{\frac{2g+3}{4g+2}} ight)...