Intrinsic characterization of hyperelliptic stable curves via involution with rational-tree quotient, valid in all characteristics and matching the moduli stack ĀH_g.
arXiv preprint arXiv:2602.16434 , year=
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Constructs moduli stacks ΓM_{g,n}^{ex,m} and M_{g,n}^{ex,m} over F_p parametrizing curves with exact meromorphic differentials of fixed divisor type and proves they are smooth with computed dimensions via a local-global deformation principle.
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Hyperelliptic Stable Curves
Intrinsic characterization of hyperelliptic stable curves via involution with rational-tree quotient, valid in all characteristics and matching the moduli stack ĀH_g.
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The Moduli Space of Twisted Exact Differential Forms on Curves in Positive Characteristic
Constructs moduli stacks ΓM_{g,n}^{ex,m} and M_{g,n}^{ex,m} over F_p parametrizing curves with exact meromorphic differentials of fixed divisor type and proves they are smooth with computed dimensions via a local-global deformation principle.