We establish a global Torelli theorem for the complete family of Calabi-Yau threefolds arising from cyclic triple covers of P^(3)branched along six stable hyperplanes.
In this paper,we study the theory of complements,introduced by Shokurov,for Calabi-Yau type varieties with the coefficient set[0,1].We show that there exists afinite set of positive integers N,such that if a threefold p...In this paper,we study the theory of complements,introduced by Shokurov,for Calabi-Yau type varieties with the coefficient set[0,1].We show that there exists afinite set of positive integers N,such that if a threefold pair(X/Z∋z,B)has an R-complement which is klt over a neighborhood of z,then it has an n-complement for some n∈N.We also show the boundedness of complements for R-complementary surface pairs.展开更多
Quantum field theory creates fermions via abstract operators exciting abstract fields, with a specific field for each type of specific particle. This operator algebra lends itself well to quantum statistics, neverthel...Quantum field theory creates fermions via abstract operators exciting abstract fields, with a specific field for each type of specific particle. This operator algebra lends itself well to quantum statistics, nevertheless, our physical understanding of this process is nonintuitive at best. In this paper we analyze the creation of fermions from primordial gauge field quantum gravity loops in the context of Calabi-Yau manifold theory. I extend a prior mass-gap treatment based on Yang-Mills gauge theory of higher order self-interaction to include the half-integral spin of fermions.展开更多
This is a survey of using NMSP method to study higher genus Gromov-Witten invariants of Calabi-Yau quintics.It emphasizes on how and why the various methods are introduced to solve several important conjectures for hi...This is a survey of using NMSP method to study higher genus Gromov-Witten invariants of Calabi-Yau quintics.It emphasizes on how and why the various methods are introduced to solve several important conjectures for higher genus Gromov-Witten invariants of Calabi-Yau quintics.展开更多
We construct an N = 2 superconformal vertex algebra（SCVA） from a generalized Calabi-Yau manifold and compute the BRST cohomology of its associated topological vertex algebras. We show that the BRST cohomology coinci...We construct an N = 2 superconformal vertex algebra（SCVA） from a generalized Calabi-Yau manifold and compute the BRST cohomology of its associated topological vertex algebras. We show that the BRST cohomology coincides with the generalized Dobeault cohomology. We show that the two topological vertex algebras constructed from the N = 2 SCVA by A and B twist respectively are mirror pairs.展开更多
Math and physics proceed from assumptions to conclusions via a logical path. Artificial intelligence possesses the ability to follow logic, herein specifically applied to the problem of defining ontologically real 2D ...Math and physics proceed from assumptions to conclusions via a logical path. Artificial intelligence possesses the ability to follow logic, herein specifically applied to the problem of defining ontologically real 2D manifolds in a 3D continuum. Vortices and tori in fluids exhibit effective 2D surfaces, which, treated as manifolds, allow application of calculus on the boundaries of the structures. Recent papers in primordial field theory (PFT) have employed Calabi-Yau geometry and topology to develop a fermion structure. We desire a logical justification of this application and herein explore the use of artificial intelligence to assist in logic verification. A proof is outlined by the author and formalized by the AI.展开更多
A theory of quantum gravity has recently been developed by the author based on the concept that all forces converge to one at the moment of Creation. This primordial field can only interact with itself, as no other fi...A theory of quantum gravity has recently been developed by the author based on the concept that all forces converge to one at the moment of Creation. This primordial field can only interact with itself, as no other field exists, contrasting with the Standard Model of Particle Physics in which each elementary particle is an excitation in its own quantum field. The primordial field theory of quantum gravity has produced a model of a fermion with a mass gap, ½-integral spin, discrete charge, and magnetic moment. The mass gap is based on an existence theorem that is anchored in Yang-Mills, while Calabi-Yau anchors ½-integral spin, with charge and magnetic moment based on duality. Based on N-windings, this work is here extended to encompass fractional charge, with the result applied to quarks, yielding fermion mass and charge in agreement with experiment and novel size correlations and a unique quantum gravity-based ontological understanding of quarks.展开更多
文摘We establish a global Torelli theorem for the complete family of Calabi-Yau threefolds arising from cyclic triple covers of P^(3)branched along six stable hyperplanes.
基金supported by the China Post-doctoral Science Foundation(Grant Nos.BX2021269 and 2021M702925)supported by National Key Research and Development Program of China(Grant No.2020YFA0713200)+1 种基金supported by NSF Research Grants(Nos.DMS-1801851 and DMS-1952522)by a grant from the Simons Foundation(Award Number:256202).
文摘In this paper,we study the theory of complements,introduced by Shokurov,for Calabi-Yau type varieties with the coefficient set[0,1].We show that there exists afinite set of positive integers N,such that if a threefold pair(X/Z∋z,B)has an R-complement which is klt over a neighborhood of z,then it has an n-complement for some n∈N.We also show the boundedness of complements for R-complementary surface pairs.
文摘Quantum field theory creates fermions via abstract operators exciting abstract fields, with a specific field for each type of specific particle. This operator algebra lends itself well to quantum statistics, nevertheless, our physical understanding of this process is nonintuitive at best. In this paper we analyze the creation of fermions from primordial gauge field quantum gravity loops in the context of Calabi-Yau manifold theory. I extend a prior mass-gap treatment based on Yang-Mills gauge theory of higher order self-interaction to include the half-integral spin of fermions.
基金Supported by Hong Kong GRF16301515,GRF16301717,GRF16304119 and GRF16306222。
文摘This is a survey of using NMSP method to study higher genus Gromov-Witten invariants of Calabi-Yau quintics.It emphasizes on how and why the various methods are introduced to solve several important conjectures for higher genus Gromov-Witten invariants of Calabi-Yau quintics.
文摘We construct an N = 2 superconformal vertex algebra（SCVA） from a generalized Calabi-Yau manifold and compute the BRST cohomology of its associated topological vertex algebras. We show that the BRST cohomology coincides with the generalized Dobeault cohomology. We show that the two topological vertex algebras constructed from the N = 2 SCVA by A and B twist respectively are mirror pairs.
文摘Math and physics proceed from assumptions to conclusions via a logical path. Artificial intelligence possesses the ability to follow logic, herein specifically applied to the problem of defining ontologically real 2D manifolds in a 3D continuum. Vortices and tori in fluids exhibit effective 2D surfaces, which, treated as manifolds, allow application of calculus on the boundaries of the structures. Recent papers in primordial field theory (PFT) have employed Calabi-Yau geometry and topology to develop a fermion structure. We desire a logical justification of this application and herein explore the use of artificial intelligence to assist in logic verification. A proof is outlined by the author and formalized by the AI.
文摘A theory of quantum gravity has recently been developed by the author based on the concept that all forces converge to one at the moment of Creation. This primordial field can only interact with itself, as no other field exists, contrasting with the Standard Model of Particle Physics in which each elementary particle is an excitation in its own quantum field. The primordial field theory of quantum gravity has produced a model of a fermion with a mass gap, ½-integral spin, discrete charge, and magnetic moment. The mass gap is based on an existence theorem that is anchored in Yang-Mills, while Calabi-Yau anchors ½-integral spin, with charge and magnetic moment based on duality. Based on N-windings, this work is here extended to encompass fractional charge, with the result applied to quarks, yielding fermion mass and charge in agreement with experiment and novel size correlations and a unique quantum gravity-based ontological understanding of quarks.
