Non-calibrated framed processes, derived equivalence and Homological Mirror Symmetry
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913059992240128 |
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| author | Rossi, Michele |
| author_facet | Rossi, Michele |
| contents | The present paper is aimed to discussing three kinds of problems:
(1) producing some ``mirror theorem'' for the recent mirror symmetric construction, called \emph{framed} duality ($f$-duality), described in \cite{R-fTV} and \cite{R-fpCI}: this is performed from the point of view proposed by Homological Mirror Symmetry (HMS), by studying \emph{derived equivalence} ($D$-equivalence) of multiple mirror models produced by means of a, so-called, \emph{uncalibrated $f$-process}; (2) proposing a general construction giving a big number of multiple mirror models to, in principle, any projective complete intersection of non-negative Kodaira dimension: these multiple mirrors turn out to be each other connected by means of uncalibrated $f$-processes and then, after (1), $D$-equivalent or $K$-equivalent, in the sense of Kawamata \cite{Kawamata}; (3) presenting a number of evidences for the Bondal-Orlov-Kawamata conjecture that $D$-equivalence is $K$-equivalence, and viceversa. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_01856 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Non-calibrated framed processes, derived equivalence and Homological Mirror Symmetry Rossi, Michele Algebraic Geometry 14J33, 14M25, 53D37 The present paper is aimed to discussing three kinds of problems: (1) producing some ``mirror theorem'' for the recent mirror symmetric construction, called \emph{framed} duality ($f$-duality), described in \cite{R-fTV} and \cite{R-fpCI}: this is performed from the point of view proposed by Homological Mirror Symmetry (HMS), by studying \emph{derived equivalence} ($D$-equivalence) of multiple mirror models produced by means of a, so-called, \emph{uncalibrated $f$-process}; (2) proposing a general construction giving a big number of multiple mirror models to, in principle, any projective complete intersection of non-negative Kodaira dimension: these multiple mirrors turn out to be each other connected by means of uncalibrated $f$-processes and then, after (1), $D$-equivalent or $K$-equivalent, in the sense of Kawamata \cite{Kawamata}; (3) presenting a number of evidences for the Bondal-Orlov-Kawamata conjecture that $D$-equivalence is $K$-equivalence, and viceversa. |
| title | Non-calibrated framed processes, derived equivalence and Homological Mirror Symmetry |
| topic | Algebraic Geometry 14J33, 14M25, 53D37 |
| url | https://arxiv.org/abs/2304.01856 |