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PreprintCC BY-NC-ND 4.0HAL

AN APPLICATION OF BINOMIAL DETERMINANTS TO THE SPACE OF ARCS

  • Ana J. Reguera
  • Miguel Valderrama
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Abstract

In this paper we present an application of Gessel and Viennot's result on binomial determinants [GV85]. We prove that the space of arcs C∞ of the normalization C of a curve C is the normalization of its space of arcs with the reduced structure. We prove this result first when C is a monomial curve, and then when C is the formal neighborhood at a closed point of an affine curve over an algebraically closed field of characteristic zero.

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Cite

BibTeXRIS
BibTeX
@misc{reguera2026application,
  title = {{AN APPLICATION OF BINOMIAL DETERMINANTS TO THE SPACE OF ARCS}},
  author = {Ana J. Reguera and Miguel Valderrama},
  howpublished = {HAL},
  year = {2026},
  month = may,
  url = {https://hal.science/hal-05733810v1},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - AN APPLICATION OF BINOMIAL DETERMINANTS TO THE SPACE OF ARCS
AU  - Ana J. Reguera
AU  - Miguel Valderrama
PY  - 2026
DA  - 2026/05/24
PB  - HAL
UR  - https://hal.science/hal-05733810v1
AB  - In this paper we present an application of Gessel and Viennot's result on binomial determinants [GV85]. We prove that the space of arcs C∞ of the normalization C of a curve C is the normalization of its space of arcs with the reduced structure. We prove this result first when C is a monomial curve, and then when C is the formal neighborhood at a closed point of an affine curve over an algebraically closed field of characteristic zero.
ER  -