What better way to commence a criminal...

What better way to commence a criminal new year than with an outstanding discovery. An Easy Thing by Paco Ignacio Taibo II, translated by William I. Neuman (Viking: $16.95; 225 pp.), has been published in Mexico and elsewhere and has been the basis for a Spanish-language film. Just now, however, the book makes its first appearance in English in a lively and colloquial translation. Well, high time.

Ignacio Taibo’s protagonist is a 31-year-old part-Basque, part-Irish independent investigator in Mexico City named Hector Belascoaran Shayne. He prefers “independent” to “private,” possibly because he has to share his crummy office with a plumber, an upholsterer and a sewer inspector, none of whom prospers.

He is involved in three cases simultaneously: an industrial murder, seemingly one of a series; chaperoning the teen-aged daughter of an oversexed porn queen, and, very romantically, trying to establish that Emiliano Zapata was not killed in ambush in 1919, as history believed, but that Zapata, in his 90s, lives on in a cave, sustained by his aging admirers.

Hector is instinctively left-wing, the child of radical socialists who met during the Spanish Civil War, his mother a sort of Celtic La Pasionara. This alone makes him unique in independent-eye circles. What makes the book unique is the author’s evocation, at once loving, despairing, acrid and vital, of Mexico City. Hector’s exhaustions are almost palpable (he gives his clients full value), his solutions explosive, his company very welcome indeed.

Another welcome discovery at the turning of the year is Virginia Anderson, whose hefty Blood Lies (Bantam Crime Line: $3.95, paper; 416 pp.) borders on Dick Francis’ turf, the world of thoroughbred breeding and training in Kentucky.

It is not surprising to learn that Anderson, who lives in Dade City, Fla., has herself raised and trained thoroughbreds. The workings of the business, from feeding to syndication, are written out of obvious and engrossing knowledge. Her central figure is a rich kid returning to work around horses again after having fled his snarling family eight years earlier.

An old track friend has died in a suspicious fire, leaving a suspiciously healthy inheritance. The murdering is not yet done, and the motivation is a horse worth millions at stud. Action abounds, and it all centers on characters, the boy especially, who have dimension, including depth. A real winner, this one.

So is Criss Cross (St. Martin’s: $17.95; 323 pp.) by Tom Takonis, whose first novel, “Michigan Roll,” was enthusiastically reviewed in 1988. The setting is Grand Rapids, where Takonis lives after an itinerant career as everything from gandy dancer to college professor.

The tough view is from the lower depths. An ex-cop named Mitch Morse has been reduced by an explosive temper to doing private security work, where the temper is causing him renewed trouble. Two ex-cons, one even dumber although not less lethal than the other, are planning an armored-van caper with another ex-con who has been running a hair-restoring scam that cannot even grow dandruff. The paths (and several other vectors, including a good woman and a bad one) collide in a long-sustained finale that is a small gem of crime- writing construction. Takonis is another name to watch.

Peter Dickinson is probably the most fanciful of English mysterians, who has built novels around an African tribe living in London, communicative apes and bizarre castles. In “King and Joker” a few years ago, he gave England a contemporary King Victor II, imagining the elder brother of George V did not, in fact, die young but lived to change the whole royal sequence.

Skeleton-in-Waiting (Pantheon: $16.95; 154 pp.) continues the royal saga-of-sorts, focusing this time on Princess Louise, her commoner husband Piers (who is into artificial intelligence, a characteristic Dickinson ploy), some scandalous diaries of a Romanov grandmother, just dead, and some terrorist threats against Victor II and family.

Dickinson is nothing if not daring. His buildup is leisurely, with significant alarums buried in the charming and incessant talk like raisins in a bun. (Teasing phone calls, caller unidentified and callee unheard, precede each chapter.) About the time the reader might be tempted to drum fingers impatiently, all royal hell breaks loose: a kidnaping, hostage-takings, shoot-outs, astonishing revelations, a grand whiz-bang finish.

Elliott Roosevelt continues his adroitly charming series of mysteries featuring his mother, Eleanor, as the crime-solver. Murder in the Rose Garden (St. Martin’s: $16.95; 232 pp.) is the seventh. A socially prominent woman is killed in the very shadow of the White House. She proves to have been blackmailing an A-list of senators and the odd judge with naughty photographs. There are more deaths before Mrs. Roosevelt, with considerable help from deferential detectives, manages to protect the innocent (her prime concern) and identify the culprit.

The enhanced interest, not quite between the lines, is in the author’s view of the F.D.R. White House, most particularly in this book an affectionate glimpse of his father’s friendship with secretary Missy Le Hand.

Roosevelt has also edited Perfect Crimes (St. Martin’s: $17.95; 224 pp.), an anthology of fine short stories, including Cornell Woolrich’s suspenseful “Three O’Clock,” a reminder of what a luridly inventive mind he had.

Mickey Spillane is still at it, and I think the word is unrepentant. He still seems to type with fists, not fingers, and what good is a novel that does not have a .45 slug splattering the baddie’s brains over the last page? Meanwhile, “His face was tight with a screaming grimace,” and so it goes. In The Killing Man (E. P. Dutton: $17.95; 228 pp.), a battered secretary, Velma, a corpse in Mike Hammer’s own chair, drugs, twinship and the ever-present CIA are other ingredients in a mix by now fairly funny, though whether by intention or not is not clear.

Novelist Robert Barnard (“Death in a Cold Climate”) writes short stories with a wicked final twist in a tradition honored by Saki, Roald Dahl and Ruth Rendell as well. Death of a Salesperson (Scribner’s: $16.95; 200 pp.) is a collection revealing just how well, and satirically, Barnard does it. Never was such an assortment of unpleasant persons so welcomely hoist via their own petards.

For the insatiable Agatha Christie faithful, tragically bereft of new material to enjoy, there is the large and wonderful body of existing work to re-explore and read yet again. The Life and Times of Hercule Poirot by Anne Hart (G. P. Putnam’s Sons: $19.95; 288 pp.) extracts all the references to the little Belgian from his first appearance in Christie’s first novel, “The Mysterious Affair at Styles,” to his last in “Curtain” (published in 1975 although written during World War II and stashed away), and makes them into a kind of biography. Hart did the same chore earlier for Jane Marple.

Also at hand is a revised edition of The Agatha Christie Companion by Dennis Sanders and Len Lovallo (Berkley: $12.95, paper; 488 pp.), subtitled “The Complete Guide to Agatha Christie’s Life and Work.” It is in fact a biography in the form of a chronological exposition of the novels, plays and stories. The appendices offer such services as lists of the books and stories in which Capt. Hastings appears. Even the insatiable may be temporarily appeased. But the proof of Christie’s overwhelming productivity is still awesome.