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Main Authors: Chekeres, Olga, Kandel, Santosh, Losev, Andrey, Mnev, Pavel, Wernli, Konstantin, Youmans, Donald R.
Format: Preprint
Published: 2023
Subjects:
Online Access:https://arxiv.org/abs/2308.06844
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author Chekeres, Olga
Kandel, Santosh
Losev, Andrey
Mnev, Pavel
Wernli, Konstantin
Youmans, Donald R.
author_facet Chekeres, Olga
Kandel, Santosh
Losev, Andrey
Mnev, Pavel
Wernli, Konstantin
Youmans, Donald R.
contents We address the question of counting maps between projective spaces such that images of cycles on the source intersect cycles on the target. In this paper we do it by embedding maps into quasimaps that form a projective space of their own. When a quasimap is not a map, it contains freckles (studied earlier) and/or scars, appearing when the complex dimension of the source is greater than one. We consider a lot of examples showing that freckle/scar calculus (using excess intersection theory) works. We also propose the "smooth conjecture" that may lead to computation of the number of maps by an integral over the space of quasimaps.
format Preprint
id arxiv_https___arxiv_org_abs_2308_06844
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle On enumerative problems for maps and quasimaps: freckles and scars
Chekeres, Olga
Kandel, Santosh
Losev, Andrey
Mnev, Pavel
Wernli, Konstantin
Youmans, Donald R.
Mathematical Physics
We address the question of counting maps between projective spaces such that images of cycles on the source intersect cycles on the target. In this paper we do it by embedding maps into quasimaps that form a projective space of their own. When a quasimap is not a map, it contains freckles (studied earlier) and/or scars, appearing when the complex dimension of the source is greater than one. We consider a lot of examples showing that freckle/scar calculus (using excess intersection theory) works. We also propose the "smooth conjecture" that may lead to computation of the number of maps by an integral over the space of quasimaps.
title On enumerative problems for maps and quasimaps: freckles and scars
topic Mathematical Physics
url https://arxiv.org/abs/2308.06844