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Elizabeth Gasparim

Short CV

Papers Published

Poster

Minicourse Lecture notes

Topology Lectures Summaries

Computational Algebraic Geometry

Research Students

Ph.D. Thesis

Masters Thesis

In Preparation

Email

Home Page

New mexico State University
Department of Mathematics
Las Cruces NM 88003
Ph: (505) 646 3901
Email: gasparim@nmsu.edu

Research Interests
  • Algebraic Geometry, Algebraic Topology, Mathematical Physics
Other Interests
Publications
  1. Local holomorphic Euler characteristic and instanton decay, with P.Majumdar ( dvi,pdf )
  2. Multiplicity of complex hypersurface singularities, Rouché satellites and Zariski's problem, with C.Eyral ( dvi, pdf )
  3. The Atiyah-Jones conjecture for rational surfaces ( dvi, pdf )
  4. Vector bundles near negative curves: moduli and local Euler characteristic, with E. Ballico ( dvi, pdf )
  5. Three applications of instanton numbers, with P. Ontaneda, to appear in Comm. Math. Phys. ( dvi, pdf )
  6. Computing Instanton numbers of curve singularities, with I. Swanson, J. Symbolic Computation 40, no.2, 965--978 (2005) ( dvi, pdf )
  7. Vector bundles on a three dimensional neighborhood of a ruled surface, with E. Ballico, J. Pure Appl. Algebra 195 no.1, 7--19 (2005) ( dvi, pdf )
  8. The Atiyah-Jones conjecture for rational surfaces, with R. J. Milgram, MPIM Bonn preprint 2004--14 (2004)
  9. Vector bundles on a neighborhood of a curve in a surface and elementary transformations, with E. Ballico, Forum Math.15 no.1, 115--122 (2003) ( dvi, pdf )
  10. Numerical invariants for bundles on blow­ups, with E. Ballico, Proc. Amer. Math. Soc. 130 no. 1, 23--32 (2002) ( dvi, pdf )
  11. Two applications of instanton numbers, Isaac Newton Inst. Preprint Series no. NI02022­ HDG, 1--15 (2002)
  12. Holomorphic vector bundles on holomorphically convex complex surfaces, with E. Ballico, Matematiche (Catania) 55 no. 1, 3--15 (2001)
  13. Chern classes of bundles on blown-up surfaces, Comm. Algebra 28 no.10, 4919--4926 (2000) ( dvi, pdf )
  14. Vector bundles on a formal neighborhood of a curve in a surface, with E. Ballico, Rocky Montain J. Math. 30 no. 3, 795--814 (2000)
  15. Holomorphic and algebraic vector bundles on 0-convex algebraic surfaces, with E. Ballico, Proc. Indian Acad. Sci. 109 no. 4, 353--358 (1999)
  16. On the topology of holomorphic bundles, Bol. Soc. Parana. Mat. 18 no. 1­2, 1--7 (1998)
  17. Rank two bundles on the blow up of C 2 , J. Algebra 199 no. 2, 581--590 (1998) ( dvi, pdf )
  18. Chern classes of bundles over rational surfaces, Instituto Politecnico di Torino Rapporto Interno 30 (1998)
  19. Holomorphic bundles on O(-k) are algebraic, Comm. Algebra 25 no. 9, 3001­3009 (1997) ( dvi, pdf )
  20. GAGA para variedades não compactas, Anais Acad. Bras. Ciências 69 no. 4 (1997)
  21. Fibrados Holomórficos sobre blow-ups, XXX Anniversary P.U.C. Peru, Pro­Math. 10 no. 20 (1996)
Minicourse Lecture notes:
  1. A first lecture on sheaf cohomology, with P. Majumdar, The Institute of Mathematical Sciences Madras, India (1998)
  2. The classification of rational surfaces, with P. Majumdar, The Institute of Mathematical Sciences Madras, India (1998), math­ph/9909010
  3. Fibração de Hopf, uma interpretação geométrica, with P. Majumdar and P. Ontaneda, Summer Lectures, Recife, Brazil (1997)
Topology Lectures Summaries:
  1. Topology I: part I - point set topology and fundamental group ( dvi, pdf )
  2. Topology I: part II - homotopy and basic differential topology ( dvi, pdf )
  3. Topology I: part III - list of Lie groups( dvi, pdf )
  4. Topology II: part I - homology theories ( dvi, pdf )
  5. Topology II: part II - De Rham cohomology ( dvi, pdf )
  6. Topology III: part I - Sheaf cohom ology ( pdf )
Computational Algebraic Geometry:
  1. Macaulay2 code used on the paper Computing Instanton Numbers of Curve Singularities (with I. Swanson) (2004)
Research Students:
  • Megan Lockwood
  • Samatha Kilroy
  • Zac Harlow
  • Pablo Gustavo Albuquerque Braz e Silva - postdoc 2001
  • Antonio Fernado Pereira de Souza - graduated 2000
Ph.D. Thesis:
  • Holomorphic rank two vector bundles on blow­ups The University of New Mexico (1995) Adviser: Charles P. Boyer
Masters Thesis:
  • Three topological invariant cardinals Universidade Estadual de Campinas, Brazil (1989) Adviser: Ofelia T. Alas
In Preparation:
  1. Vector bundles and flops.
  2. Moduli of bundles on products of curves, with C. Teleman.
  3. Surgery for holomorphic bundles.