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Aleksey Zinger
Department of Mathematics
Stony Brook |
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Publications and Preprints
The papers below are listed in the chronological order within each topic
(the topic classification is a bit arbitrary in some cases).
For non-technical descriptions of some of my work, please see
Research Highlights.
For short summaries of all papers and a diagram of connections between the papers,
please see the .pdf version
of Publication and Preprints.
Some of the older .pdf files below may be difficult to read on the screen,
but they still should print out fine.
Real Gromov-Witten Theory and Enumerative Geometry
- Counting genus zero real curves
in symplectic manifolds, Part II
joint with M. Farajzadeh Tehrani, math/1205.1809, 2 figures,
Geom. Top. 20 (2016), no. 2, 629-695
- The moduli space of maps with crosscaps:
Fredholm theory and orientability
joint with P. Georgieva, math/1301.1074, 1 figure,
Comm. Anal. Geom. 23 (2015), no. 3, 81-140
- The moduli space of maps with crosscaps:
the relative signs of the natural automorphisms
joint with P. Georgieva, math/1308.1345,
J. Symplectic Geom. 14 (2016), no. 2, 359-430
- Orientability in real Gromov-Witten theory
joint with P. Georgieva, math/1308.1347, 25 pages, 3 figures
- Enumeration of real curves in CP2n-1
and a WDVV relation for real Gromov-Witten invariants
joint with P. Georgieva, math/1309.4079, 7 figures, 3 tables,
Duke Math. 166 (2017), no. 17, 3291-3347
- A recursion for counts of real curves
in CP2n-1: another proof
joint with P. Georgieva, math/1401.1750, 3 figures,
Internat. J. Math. 29 (2018), no. 4, 1850027, 21pp
- Real Gromov-Witten theory in all genera
and real enumerative geometry: construction
joint with P. Georgieva, math/1504.06617, 48 pages, 5 figures,
to appear in Ann. Math. 188 (2018), no. 3
Appendix computing one such invariant
Extended Abstract (for Penka's Oberwolfach talk):
Oberwolfach Report 27/2006, 1643-1645
- Real Gromov-Witten theory in all genera
and real enumerative geometry: properties
joint with P. Georgieva, math/1507.06633, 55 pages,
to appear in J. Symplectic Geom.
- Real Gromov-Witten theory in all genera
and real enumerative geometry: computation
joint with P. Georgieva, math/1510.07568, 66 pages, 3 figures,
to appear in J. Diff. Geom.
- Lower bounds for enumerative counts
of positive-genus real curves
joint with J. Niu, math/1511.02206, 49 pages, 3 figures, 2 tables
Appendix computing low-genus
low-degree real Gromov-Witten invariants
Jingchen's poster for AGNES, October 2015
- On the topology of real bundle pairs over nodal symmetric
surfaces
joint with P. Georgieva, math/1512.07216, 3 figures, Topology Appl. 214 (2016), 109-126
- Real orientations, real Gromov-Witten theory, and real
enumerative geometry
joint with P. Georgieva, math/1512.07220, ERA MS 24 (2017), 87-99
- Real Ruan-Tian perturbations
math/1701.01420, 50 pages, 2 figures
General Symplectic Topology
- Normal crossings singularities for symplectic topology
joint with M. Tehrani and M. McLean, math/1410.0609, 65 pages, 6 figures
- The smoothability of normal crossings symplectic varieties
joint with M. Tehrani and M. McLean, math/1410.2573, 59 pages, 4 figures
- Normal crossings degenerations of symplectic manifolds
joint with M. Tehrani, math/1603.07661, 65 pages, 2 figures
- Singularities and semistable degenerations for symplectic topology
joint with M. Tehrani and M. McLean, math/1707.01464, 2 figures
C. R. Math. Acad. Sci. Paris 356 (2018), no. 4, 420-432
Foundations of Gromov-Witten Theory
- Pseudocycles and integral homology
math.AT/0605535, 2 figures, Trans. AMS 360 (2008), no. 5, 2741-2765
Older, more technical/direct version:
math.AT/0605535v1, 37 pages, 3 figures
- A comparison theorem for Gromov-Witten invariants
in the symplectic category
math/0807.0805, Adv. Math. 228 (2011), no. 1, 535--574
- On transverse triangulations
math/1012.3979, Munster J. Math. 5 (2012), 99-106
- The determinant line bundle for Fredholm operators:
construction, properties, and classification
math/1304.6368, Math. Scand. 118 (2016), no. 2, 203--268
Updated version
- On symplectic sum formulas in Gromov-Witten theory (updated 12/28/14)
joint with M. Tehrani, 91 pages, 6 figures, math/1404.1898
Version from 03/14/14 (pre-arXiv);
Updates 02/26/15;
Related e-mails
Li-Ruan's arXiv response
(with my comments in red italics in smaller print and at the end)
More on the Li-Ruan situation
Comments on Ionel-Parker's response
- Absolute vs. relative Gromov-Witten invariants
joint with M. Tehrani, math/1405.2045, 46 pages, 11 figures, 4 tables,
J. Symplectic Geometry, 14 (2016), no. 2, 1189-1250
- On the rim tori refinement of relative Gromov-Witten invariants
joint with M. Tehrani, math/1412.8204, 43 pages
- On the refined symplectic sum formula
for Gromov-Witten invariants
joint with M. Tehrani, math/1412.8205, 54 pages
- Notes on J-holomorphic maps
math/1706.00331, 52 pages, 11 figures
Mirror Symmetry
- Genus-zero two-point hyperplane integrals
in the Gromov-Witten theory
math/0705.2725, 4 figures, Comm. Anal. Geom. 17 (2010), no. 5, 1-45
- The reduced genus-one Gromov-Witten
invariants of Calabi-Yau hypersurfaces
math/0705.2397, 5 figures, JAMS 22 (2009), no. 3, 691-737
- Some properties of hypergeometric series associated
with mirror symmetry
joint with D. Zagier, math/0710.0889,
Modular Forms and String Duality, Fields Inst. Commun. 54 (2008), 163-177
- Mirror formulas for closed, open, and unoriented
Gromov-Witten invariants
joint with A. Popa, math/1010.1946, 2 figures, 5 tables,
Adv. Math. 259 (2014), 448-510
- The genus 0 Gromov-Witten invariants of
projective complete intersections
math/1106.1633, 3 fugures, 4 tables,
Geom. Top. 18 (2014), no. 2, 1035-1114
- Mirror symmetry for stable quotients invariants
joint with Y. Cooper, math/1201.6350, 6 figures, 1 table,
Mich. Math. J. 63 (2014), no. 3, 571-621
- Double and triple Givental's J-functions for
stable quotients invariants
math/1305.2142, 9 figures, 1 table,
Pacific J. Math. 272 (2014), no. 2, 439-507
- Energy bounds and vanishing results for
the Gromov-Witten invariants of the projective space
math/1801.07242, 57 pages, 4 figures
- Equivariant Localization and Mirror Symmetry
course notes inspired by Pandharipande's notes on Givental's proof of mirror symmetry
for the quintic, in preparation whenever I teach this course;
Chapters 1 and 4 and the beginning of Chapter 2 should be complete,
but there is not much beyond that
Topology of Moduli Spaces of Pseudoholomorphic Maps
- A sharp compactness theorem for genus-one
pseudo-holomorphic maps
math.SG/0406103, 7 figures, Geom. Top. 13 (2009), no. 5, 2427-2522
Some comments, 2 pages
- On the structure of certain natural cones over moduli
spaces of genus-one holomorphic maps
math.SG/0406104, 3 figures, Adv. Math. 214 (2007), no. 2, 878-933
- On the genus-one Gromov-Witten invariants
of a quintic threefold
joint with J. Li, math.AG/0406105, 5 figures, Pacific J. Math 233 (2007), no. 2, 417-480
- Reduced genus-one Gromov-Witten invariants
math.SG/0507103, 5 figures, JDG 83 (2009), no. 2, 407-460
- On the genus-one Gromov-Witten invariants of
complete intersections
joint with J. Li, math.AG/0507104, 4 figures, 1 table,
JDG 82 (2009), no. 3, 641-690
- A desingularization of the main component of
the moduli space of genus-one stable maps into Pn
joint with R. Vakil, math.AG/0603353, 13 figures, Geom. Top. 12 (2008), 1-95
Overview (independent): 2 figures, ERA AMS 13 (2007), 53-59
Extended Abstract (for Ravi's Oberwolfach talk):
Oberwolfach Reports 27/2006, 1643-1645
- Intersections of tautological classes on
blowups of moduli spaces of genus-one curves
math.AG/0603357, 5 figures, Mich. Math. 55 (2007), no 3, 535-560
- Standard vs. reduced genus-one Gromov-Witten invariants
math/0706.0715, Geom. Top. 12 (2008), no. 2, 1203-1241
Local Excess Intersection Approach
- Completion of Katz-Qin-Ruan's enumeration of genus-two
plane curves
math.AG/0201216, 3 figures, 1 table,
J. Algebraic Geom. 13 (2004), no. 3, 547-561
- Enumerative vs. symplectic invariants
and obstruction bundles
math.SG/0201255, J. Symplectic Geom. 2 (2004), no. 4, 445--543
- Enumeration of genus-two curves with a fixed
complex structure in P2 and P3
math.SG/0201254, 2 figures, 3 tables, J. Diff. Geom. 65 (2003), no. 3, 341-467
- Enumeration of genus-three plane curves with
a fixed complex structure
math.SG/0203058, 3 tables, J. Algebraic Geom. 14 (2005), no. 1, 35-81
- Enumeration of one-nodal rational curves
in projective spaces
math.AG/0204236, 9 figures, 1 table,
Topology 43 (2004), no. 4, 793-829
- Counting rational curves of arbitrary shape
in projective spaces
math.AG/0210146, 15 figures, 5 tables, Geom. Top. 9 (2005), 571-697
- Enumerative geometry of Calabi-Yau 5-folds
joint with R. Pandharipande, math/0802.1640, 6 figures, 3 tables,
New Developments in Algebraic Geometry, Integrable Systems and Mirror Symmetry,
ASPM 59 (2010), 239-288
Appendix (self-contained), 6 pages
Miscellaneous
- The exponential decay rate of the lower bound for
the first eigenvalue of compact manifolds
joint with M. Kalka, E. Mann, and D. Yang,
1 figure, Internat. J. Math. 8 (1997), no. 3, 345--355
-
Enumerative algebraic geometry via techniques of
symplectic topology and analysis of local obstructions
Ph.D. Thesis, MIT 2002, 240 pages, 8 tables
- Counting plane rational curves: old and new approaches
math.AG/0507105, expository notes, 32 pages, 2 figures, 2 tables
- Basic Riemannian geometry and Sobolev estimates
used in symplectic topology
math/1012.3980, expository notes, 33 pages, 3 figures
- On the robustness of extortionate strategies
in iterated Prisoner's Dilemma
joint with J. Chen, 5 figures, 6 tables,
J. Theor. Bio., 357 (2014), 46-54
- Some conjectures on
the asymptotic behavior of Gromov-Witten invariants
math/1610.02971, 26 pages, 1 figure; old version
- Some questions in the theory of pseudoholomorphic curves
math/1805.09647, 28 pages, 4 figures
- Foundations of Smooth Manifolds and Vector Bundles
course notes inspired by Warner's book, in preparation whenever I teach this course;
the first two chapters should be complete, but there is not much beyond that
This page is maintained by
Aleksey Zinger.
Last modified: August 15, 2017.