Contact Cohomology of the Projective Plane

Lars Ernström, Gary J. Kennedy

Type: Article

Publication Date: 1999-02-01

Citations: 15

DOI: https://doi.org/10.1353/ajm.1999.0004

Abstract

We construct an associative ring which is a deformation of the quantum cohomology ring of the projective plane. Just as the quantum cohomology encodes the incidence characteristic numbers of rational plane curves, the contact cohomology encodes the tangency characteristic numbers.

Locations

American Journal of Mathematics - View
arXiv (Cornell University) - View - PDF

Similar Works

Action	Title	Year	Authors
+	Contact Cohomology of the Projective Plane	1997	Lars Ernström Gary W. Kennedy
+	Contact Cohomology of the Projective Plane	1997	Lars Ernström Gary J. Kennedy
+	Noncommutative complex geometry of the quantum projective space	2011	Masoud Khalkhali Ali Moatadelro
+ PDF Chat	Geometry of Quantum Projective Spaces	2013	Francesco D’Andrea Giovanni Landi
+	Quantum cohomology of the Hilbert scheme of points in the plane	2004	Andreĭ Okounkov Rahul Pandharipande
+ PDF Chat	Tangency quantum cohomology	2003	Joachim Kock
+	Gamma classes and quantum cohomology	2023	Hiroshi Iritani
+	The Picard Group of a Noncommutative Algebraic Torus	2010	Yuri Berest Ajay C. Ramadoss Xiang Tang
+ PDF Chat	The Grothendieck group of a quantum projective space bundle	2006	Izuru Mori S. Paul Smith
+	Tangency quantum cohomology	2000	Joachim Kock
+	Tangency quantum cohomology	2000	Joachim Kock
+	Equivariant functions and rational differential operators	2019	Michael Deutsch
+	Equivariant functions and rational differential operators	2019	Michael Deutsch
+ PDF Chat	Quantum cohomology of the Hilbert scheme of points in the plane	2009	Andreĭ Okounkov Rahul Pandharipande
+	Gamma classes and quantum cohomology	2023	Hiroshi Iritani
+ PDF Chat	Quantum deformations of projective three-space	2015	Brent Pym
+	Complex projective geometry and quantum projective field theory	1994	D. V. Yur’ev
+	The homogeneous coordinate ring of the quantum projective plane	2010	Masoud Khalkhali Ali Moatadelro
+ PDF Chat	Holomorphic Structures on the Quantum Projective Line	2010	Masoud Khalkhali Giovanni Landi Walter D. van Suijlekom
+	Quantum McKay Correspondence and Equivariant Sheaves on the Quantum Projective Line	2012	Alexander Kirillov Jaimal Thind

Works That Cite This (15)

Action	Title	Year	Authors
+	Recursions, formulas, and graph-theoretic interpretations of ramified coverings of the sphere by surfaces of genus 0 and 1	1998	Ravi Vakil
+	Gromov-Witten theory of Deligne-Mumford stacks	2006	Dan Abramovich Tom Graber Angelo Vistoli
+	Recursion for twisted descendants and characteristic numbers of rational curves	1999	Joachim Kock
+ PDF Chat	Generalizing Tropical Kontsevich's Formula to Multiple Cross-Ratios	2020	Christoph Goldner
+ PDF Chat	Genus $0$ and $1$ Hurwitz numbers: Recursions, formulas, and graph-theoretic interpretations	2001	Ravi Vakil
+ PDF Chat	Tangency quantum cohomology and characteristic numbers	2001	Joachim Kock
+ PDF Chat	Tangential Quantum Cohomology of Arbitrary Order	2008	Susan Jane Colley Gary J. Kennedy
+ PDF Chat	Tangency quantum cohomology	2003	Joachim Kock
+ PDF Chat	Recursions for characteristic numbers of genus one plane curves	2001	Ravi Vakil
+	Generalizing tropical Kontsevich's formula to multiple cross-ratios	2020	Christoph Goldner

Works Cited by This (8)

Action	Title	Year	Authors
+	On the Quantum Cohomology of Homogeneous Varieties	2004	William Fulton
+ PDF Chat	Enumeration of Rational Curves Via Torus Actions	1995	Maxim Kontsevich
+	Recursive Formulas for the Characteristic Numbers of Rational Plane Curves	1996	Lars Ernström Gary J. Kennedy
+ PDF Chat	Quantum Intersection Rings	1995	Philippe Di Francesco C. Itzykson
+	The quantum cohomology of homogeneous varieties	1995	Jun Li Gang Tian
+	Stacks of stable maps and Gromov-Witten invariants	1996	Kai Behrend Yu. I. Manin
+	Intersection theory on algebraic stacks and on their moduli spaces	1989	Angelo Vistoli
+ PDF Chat	Gromov-Witten classes, quantum cohomology, and enumerative geometry	1994	Maxim Kontsevich Yu. I. Manin