On algebraic curves $$$$ of genus zero
Sign Up to like & getrecommendations! Published in 2018 at "Mathematische Zeitschrift"
DOI: 10.1007/s00209-017-1889-9
Abstract: Using a geometric approach involving Riemann surface orbifolds, we provide lower bounds for the genus of an irreducible algebraic curve of the form $$\mathcal {E}_{A,B}:\, A(x)-B(y)=0$$ , where $$A, B\in \mathbb {C}(z)$$ . We also… read more here.
Keywords: genus zero; algebraic curves; curves genus;
Genus zero Gopakumar–Vafa type invariants for Calabi–Yau 4-folds
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DOI: 10.1016/j.aim.2018.08.013
Abstract: Abstract In analogy with the Gopakumar–Vafa conjecture on CY 3-folds, Klemm and Pandharipande defined GV type invariants on Calabi–Yau 4-folds using Gromov–Witten theory and conjectured their integrality. In this paper, we propose a sheaf-theoretic interpretation… read more here.
Keywords: genus zero; calabi yau; yau folds; type invariants ... See more keywords
Closed strings as single-valued open strings: a genus-zero derivation
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Physics A: Mathematical and Theoretical"
DOI: 10.1088/1751-8121/aaea14
Abstract: Based on general mathematical assumptions we give an independent, elementary derivation of a theorem by Francis Brown and Cl\'ement Dupont which states that tree-level amplitudes of closed and open strings are related through the single-valued… read more here.
Keywords: genus zero; open strings; single valued; derivation ... See more keywords